Sample QuestionsArithmetic Progression questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the arithmetic mean of:
3x - 2y and 3x + 2y
Find the arithmetic mean of -5 and 41.
Insert one arithmetic mean between 3 and 13.
The $n^{th}$ term of a sequence is $8 - 5$n. Show that the sequence is an $A.P.$
View full solution →Find the sum of first $20$ terms of an A.P. whose first term is $3$ and the last term is $57.$
View full solution →Find the sum of first 10 terms of the A.P. $4 + 6 + 8 + .......$
View full solution →Find the arithmetic mean of:
$(m + n)^2$ and $(m - n)^2$
View full solution →How many multiples of $4$ lie between $10$ and $250?$
View full solution →Find the general term ($n^{th}$ term) and $23^{rd}$ term of the sequence$ 3, 1, -1, -3, ….. .$
View full solution →An A.P. consists of 50 terms of which $3^{\text {rd }}$ term is 12 and the last term is 106 . Find the $29^{\text {th }}$ term of the A.P.
View full solution →If the third and the $9^{th}$ term of an A.P. be $4$ and $-8$ respectively, find which term is zero?
View full solution →Find the sum of last 8 terms of the A.P. $-12, -10, -8, ……, 58.$
View full solution →Can $2 n^2-7$ be the $n^{\text {th }}$ term of an $A.P?$ Explain.
View full solution →Find five numbers in A.P whose sum is $12 \frac{1}{2}$ and the ratio of the first to the last terms $2:3.$
View full solution →Divide $96$ into four parts which are in A.P and the ratio between product of their means to product of their extremes is $15:7.$
View full solution →The sum of three consecutive terms of an A.P. is $21$ and the sum of their squares is $165.$ find these terms.
View full solution →If the sum of first $7$ terms of an A.P. is $49$ and that of its first $17$ terms is $289,$ find the sum of first n terms of the A.P.
View full solution →The fourth term of an $A.P.$ is $11$ and the term exceeds twice the fourth term by $5$ the $A.P$ and the sum of first $50$ terms.
View full solution →How many terms of the series $18 + 15 + 12 + ……..$ when added together will give $45?$
View full solution →The first term of an A.P. is $20$ and the sum of its first seven terms is $2100;$ find the $31^{st}$ term of this A.P.
View full solution →Find the sum of the A.P., $14, 21, 28, …, 168.$
View full solution →For an A.P., show that:
$(m + n)^{th} ~term + (m - n)^{th} ~term = 2 \times m^{th} ~term$
View full solution →The sum of first $14$ terms of an A.P. is $1050$ and its $14^{th}$ term is $140$. Find the $20^{th}$ term.
View full solution →The $7^{\text {th }}$ term of the given Arithmetic Progression (A.P.):
$\frac{1}{a},\left(\frac{1}{a}+1\right) \cdot\left(\frac{1}{a}+2\right), \ldots$ is
- ✓
$\left(\frac{1}{a}+6\right)$
- B
$\left(\frac{1}{a}+7\right)$
- C
$\left(\frac{1}{a}+8\right)$
- D
$\left(\frac{1}{a}+7^7\right)$
Answer: A.
View full solution →The $n^{\text {th }}$ term of an Arithmetic Progression (A.P.) is $2 n+5$. The $10^{\text {th }}$ term is:
Answer: C.
View full solution →Statement (A): The 10th term of the AP $8,10,12, \ldots 126$ is 36
Statement (B): The sum of the 10th terms of the AP 8, 10, 12, ..., 126 is 170
Which of the statement is valid?
Answer: B.
View full solution →Statement (A): The first term and the common difference of the A.P. $2,7,12, \ldots \ldots$ is 2 and 5 respectively.
Statement (B): The 10th term of the A.P. 2, 7, $12 \ldots$ is 47
Which of the statement is valid?
Answer: C.
View full solution →Which of the following is/are an Arithmetic Progression (A.P.)?
$1.1,4,9,16$,.........
2. $\sqrt{3}, 2 \sqrt{3}, 3 \sqrt{3}, 4 \sqrt{3}$..........
3.8,6,4,2, ..........
Answer: C.
View full solution →Assertion : The sum of the first hundred natural numbers, divisible by 5 , is 25250 .
Reason : The sum of first $n$ terms of an A.P. is given by $\frac{n}{2}(a+l)$, where, $l$ is the last term.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- ✓
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: B.
View full solution →Assertion : If fourth term of an A.P. is zero, then its $25^{\text {th }}$ term is three times its $11^{\text {th }}$ term.
Reason : The sum of first $n$ terms of an A.P. is given by $\frac{n}{2}(a+l)$, where, $l$ is the last term.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- ✓
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: B.
View full solution →Assertion: The number of terms to be taken in the A.P. $9,17,25, \ldots$ So as to make a sum of 636 is 13.
Reason : The sum of first $n$ terms of an A.P. is given by $\frac{n}{2}[2 a+(n-1) d]$.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- ✓
Assertion is incorrect but reason is correct.
Answer: D.
View full solution →Assertion : The sum of $2^{\text {nd }}$ and $7^{\text {th }}$ terms of an A.P. is 30 . If its $15^{\text {th }}$ term is 1 less than twice its $8^{\text {th }}$ term, then the A.P. is $1,5,9,13,17, \ldots$
Reason : The $n^{\text {th }}$ term of an A.P. is given by $a+(n-1) d$, where $a$ and $d$ are the first term and the common difference respectively.
- ✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: A.
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