If the decreasing GP is considered, then the sum of infinite terms is:
- A64
- B128
- C256
- D729
Question types
Sequences and Series question types
280 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
280
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
156 Q→02True False[1 Marks ]
5 Q→031 Marks Question
20 Q→042 Marks Questions
22 Q→053 Marks Question
54 Q→065 Marks Questions
5 Q→07Assertion (A) & Reason (B) MCQ
16 Q→08Case study (4 Marks)
2 Q→Sample Questions
Sequences and Series questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
if an A.P. is 3,5,7,9……. Find the 12th term of the A.P.
- A12
- B21
- C22
- D25
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, the its common ratio is:
- A$\frac{1}{10}$
- B$\frac{1}{11}$
- C$\frac{1}{9}$
- D$\frac{1}{20}$
If a, b, c are in A.P. and x, y, z are in G.P., then the value of xb-c yc-a za-b is:
- A0
- B1
- Cx y z
- Dxa yb zc
If 3rd term of an A.P. is 6 and 5th term of that A.P. is 12. Then find the 21st term of that A.P.
- A40
- B42
- C60
- D63
State whether statement are True or False.
If the sum of n terms of a sequence is quadratic expression, then it always represents an A.P.
If the sum of n terms of a sequence is quadratic expression, then it always represents an A.P.
State whether statement are True or False.
The sum or difference of two G.P.s, is again a G.P.
The sum or difference of two G.P.s, is again a G.P.
State whether statement are True or False.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
State whether statement are True or False.
Two sequences cannot be in both A.P. and G.P. together.
Two sequences cannot be in both A.P. and G.P. together.
State whether statement are True or False.
Every progression is a sequence but the converse i.e., every sequence is also a progression need not necessarily be true.
Every progression is a sequence but the converse i.e., every sequence is also a progression need not necessarily be true.
Find the 10th and nth terms of the G.P. 5, 25,125,….
Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.
The income of a person is ₹3,00,000, in the first year and he receives an increase of ₹10,000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
The sum of n terms of two Arithmetic Progression are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms.
If the sum of n terms of an A.P. is $n \mathrm{P}+\frac{1}{2} n(n-1) \mathrm{Q}$, where P and Q are constants, find the common difference.
View full solution →A manufacturer reckons that the value of a machine, which cost him ₹ 15625 will depreciate each year by 20%. Find the estimated value at the end of 5 years.
For what values of x, the numbers $ \frac { - 2 } { 7 } , x , \frac { - 7 } { 2 }$ are in G.P.?
View full solution →Which term of the sequence $\frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 }$, ... is $\frac { 1 } { 19683 }$?
View full solution →Which term of the sequence 2, 2$\sqrt 2$, 4, .... is 128?
View full solution →The 4th term of a G.P. is square of its second term and the first term -3. Determine its 7th term.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2 respectively. Find the last term and the number of terms.
If f is a function satisfying f (x+y) = f (x) f (y) for all x, y $ \in $ N such that f (1) = 3 and $\sum\limits_{x = 1}^n f (x) = 120$ find the value of n.
View full solution →Find the sum of all two digit numbers which when divided by 4, yield 1 as remainder.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Show that $\frac { 1 \times 2 ^ { 2 } + 2 \times 3 ^ { 2 } + \ldots \ldots + n \times ( n + 1 ) ^ { 2 } } { 1 ^ { 2 } \times 2 + 2 ^ { 2 } \times 3 + \ldots \ldots + n ^ { 2 } ( n + 1 ) } = \frac { 3 n + 5 } { 3 n + 1 }$
View full solution →Find the sum of the following series up to n terms: $\frac { 1 ^ { 3 } } { 1 } + \frac { 1 ^ { 3 } + 2 ^ { 3 } } { 1 + 3 } + \frac { 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } } { 1 + 3 + 5 } + \ldots \ldots$
View full solution →If S1, S2, S3 are the sum of first n natural no. their squares and their cubes respectively, show that $9 S _ { 2 } ^ { 2 } = S _ { 3 } \left( 1 + 8 S _ { 1 } \right)$.
View full solution →If a, b, c are in A.P.; b, c, d are in G.P. and $\frac { 1 } { c } , \frac { 1 } { d } , \frac { 1 } { e }$ are in A.P., prove that a, c, e are in G.P.
View full solution →The ratio of the A.M. and G.M. of two positive numbers a and b is 
Show that $a : b = \left( \begin{array} { c } { m + \sqrt { m ^ { 2 } - n ^ { 2 } } } \end{array} \right) : \left( m - \sqrt { m ^ { 2 } - n ^ { 2 } } \right)$
View full solution → Show that $a : b = \left( \begin{array} { c } { m + \sqrt { m ^ { 2 } - n ^ { 2 } } } \end{array} \right) : \left( m - \sqrt { m ^ { 2 } - n ^ { 2 } } \right)$Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) The fourth term of a GP is the square of its second term and the first term is -3, then its 7th term is equal to 2187.
Reason (R) Sum of first 10 terms of the AP 6, 8, 10, ..... is equal to 150.
Assertion (A) The fourth term of a GP is the square of its second term and the first term is -3, then its 7th term is equal to 2187.
Reason (R) Sum of first 10 terms of the AP 6, 8, 10, ..... is equal to 150.
- A is true, R is true; R is acorrect explanation of A.
- A is true, R is true; R is not a correct explanation of A.
- A is true; R is false
- A is false; R is true.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) The sum of first n terms of the series 0.6 + 0.66 + 0.666 +....... is $\frac{3}{2}\Big[\text{n}-\frac{1}{9}\Big(1-\frac{1}{10}\Big)\Big].$
Reason (R) General term of a GP is Tn = arn-1, where a = first term and r =common ratio.
View full solution →Assertion (A) The sum of first n terms of the series 0.6 + 0.66 + 0.666 +....... is $\frac{3}{2}\Big[\text{n}-\frac{1}{9}\Big(1-\frac{1}{10}\Big)\Big].$
Reason (R) General term of a GP is Tn = arn-1, where a = first term and r =common ratio.
- A is true, R is true; R is acorrect explanation of A.
- A is true, R is true; R is not a correct explanation of A.
- A is true; R is false
- A is false; R is true.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) The first three terms of the sequence are $\frac{3}{2},\text{x},\frac{21}{2}$ whose nth term is $\text{a}_\text{n}=\frac{\text{n}(\text{n}^2+5)}{4}.$Then $\text{x}=\frac{9}{2}$
Reason (R) The third term of the sequence whose nth term is $\text{a}_\text{n}=(-1)^\text{n-1}5^\text{n+1}$ is 620.
View full solution →Assertion (A) The first three terms of the sequence are $\frac{3}{2},\text{x},\frac{21}{2}$ whose nth term is $\text{a}_\text{n}=\frac{\text{n}(\text{n}^2+5)}{4}.$Then $\text{x}=\frac{9}{2}$
Reason (R) The third term of the sequence whose nth term is $\text{a}_\text{n}=(-1)^\text{n-1}5^\text{n+1}$ is 620.
- A is true, R is true; R is acorrect explanation of A.
- A is true, R is true; R is not a correct explanation of A.
- A is true; R is false
- A is false; R is true.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) first and second terms of same sequence are 2 and 7 repectively.
Reason (R) Third and fourt terms of same sequence are 16 and 29. respectively.
Assertion (A) first and second terms of same sequence are 2 and 7 repectively.
Reason (R) Third and fourt terms of same sequence are 16 and 29. respectively.
- Both assertion and reason are true and reason is the correct explanation of assertion.
- Both assertion and reason are true but reason is not the correct explanation of assertion.
- Assertion is true but reason is false.
- Assertion is false but reason is true
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) The sum of the series $\frac{3}{\sqrt{5}}+\frac{4}{\sqrt{5}}+\sqrt{5}....25$ terms is $75\sqrt{5}.$
Reason (R) If 27, x, 3 are in GP, then $\text{x}=\pm\ 4.$
View full solution →Assertion (A) The sum of the series $\frac{3}{\sqrt{5}}+\frac{4}{\sqrt{5}}+\sqrt{5}....25$ terms is $75\sqrt{5}.$
Reason (R) If 27, x, 3 are in GP, then $\text{x}=\pm\ 4.$
- A is true, R is true; R is acorrect explanation of A.
- A is true, R is true; R is not a correct explanation of A.
- A is true; R is false
- A is false; R is true.
Each side of an equilateral triangle is $24 \mathrm{~cm}$. The mid-point of its sides are joined to form another triangle. This process is going continuously infinite.
Based on above information, answer the following questions.
(i) The side of the 5th triangle is (in $\mathrm{cm}$)
(a) 3 (b) 6 (c) 1.5 (d) 0.75
(ii) The sum of perimeter of first 6 triangle is (in $\mathrm{cm}$)
(a) $\frac{569}{4}$ (b) $\frac{567}{4}$ (c) 120 (d) 144
(iii) The area of all the triangle is (in sq $\mathrm{cm}$ )
(a) 576 (b) $192 \sqrt{3}$ (c) $144 \sqrt{3}$ (d) $169 \sqrt{3}$
(iv) The sum of perimeter of all triangle is (in $\mathrm{cm}$ )
(a) 144 (b) 169 (c) 400 (d) 625
(v) The perimeter of 7 th triangle is (in $\mathrm{cm}$ )
(a) $\frac{7}{8}$ (b) $\frac{9}{8}$ (c) $\frac{5}{8}$ (d) $\frac{3}{4}$
View full solution →Based on above information, answer the following questions.
(i) The side of the 5th triangle is (in $\mathrm{cm}$)
(a) 3 (b) 6 (c) 1.5 (d) 0.75
(ii) The sum of perimeter of first 6 triangle is (in $\mathrm{cm}$)
(a) $\frac{569}{4}$ (b) $\frac{567}{4}$ (c) 120 (d) 144
(iii) The area of all the triangle is (in sq $\mathrm{cm}$ )
(a) 576 (b) $192 \sqrt{3}$ (c) $144 \sqrt{3}$ (d) $169 \sqrt{3}$
(iv) The sum of perimeter of all triangle is (in $\mathrm{cm}$ )
(a) 144 (b) 169 (c) 400 (d) 625
(v) The perimeter of 7 th triangle is (in $\mathrm{cm}$ )
(a) $\frac{7}{8}$ (b) $\frac{9}{8}$ (c) $\frac{5}{8}$ (d) $\frac{3}{4}$
A company produces 500 computers in the third year and 600 computers in the seventh year. Assuming that the production increases uniformly by a constant number every year.
Based on the above information, answer the following questions.
(i) The value of the fixed number by which production is increasing every year is
(a) 25 (b) 20 (c) 10 (d) 30
(ii) The production in first year is
(a) 400 (b) 250 (c) 450 (d) 300
(iii) The total production in 10 years is
(a) 5625 (b) 5265 (c) 2655 (d) 6525
(iv) The number of computers produced in 21 st year is
(a) 650 (b) 700 (c) 850 (d) 950
(v) The difference in number of computers produced in 10th year and 8th year is
(a) 25 (b) 50 (c) 100 (d) 75
Based on the above information, answer the following questions.
(i) The value of the fixed number by which production is increasing every year is
(a) 25 (b) 20 (c) 10 (d) 30
(ii) The production in first year is
(a) 400 (b) 250 (c) 450 (d) 300
(iii) The total production in 10 years is
(a) 5625 (b) 5265 (c) 2655 (d) 6525
(iv) The number of computers produced in 21 st year is
(a) 650 (b) 700 (c) 850 (d) 950
(v) The difference in number of computers produced in 10th year and 8th year is
(a) 25 (b) 50 (c) 100 (d) 75
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