Sum of first $n$ terms of AP are $a, 3 a, 5 a$... their sum is __________
- A$n a$
- B$(2 n-1) a$
- ✓$n^2 a$
- D$n^2 a^2$
Answer: C.
View full solution →Question types
Progressions question types
173 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
173
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
47 Q→02Fill In The Blanks[1 Marks ]
2 Q→03True False[1 Marks ]
11 Q→041 Marks Question
29 Q→052 Marks Questions
39 Q→063 Marks Question
45 Q→Sample Questions
Progressions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $n^{\text {th }}$ term of an AP is $2 n+1$ then its sum of $n$ terms is ________
- A$n(n-2)$
- ✓$n(n+2)$
- C$n(n+1)$
- D$n(n-1)$
Answer: B.
View full solution →The common difference of two AP is identical and difference of their ten lakhs term is $11222333$ . Then difference of their $100^{\text {th }}$ term is _______
- ✓$11222333$
- B$333222111$
- C$222333111$
- D$333111222$
Answer: A.
View full solution →$10^{\text {th }}$ term of an AP $\sqrt{2}, \sqrt{8}, \sqrt{18}, \ldots$ is _________
- A$\sqrt{162}$
- ✓$\sqrt{200}$
- C$\sqrt{242}$
- D$\sqrt{288}$
Answer: B.
View full solution →If $+2,4-6,3-2$ are consecqutive terms of AP then = ________
- A$1$
- B$-1$
- ✓$3$
- D$29$
Answer: C.
View full solution →$k^{\text {th }}$ term of on AP $1,5,9,13$ is $45$ then find the value of $k=$ _________ $(21,11,12)$
View full solution →The sum of $2 n$ terms of an AP 2, $5,8 \ldots$ is $S _1$ and The sum of $n$ terms is $S _2$ If $S _1= S _2$ then find $n$=_____________ $(101,11,21)$
View full solution →The arithmetic sum of first $n$ odd natural number is $n(n+1)$.
View full solution →$\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots$ is an arithmetic sequence.
View full solution →$3,3,3,3, \ldots \ldots \ldots .$. is an AP
View full solution →Sum of ₹ 10,000 is deposited in bank at the rate of $8 \%$ per annual on an compound interest. Then amount depoisted in each year in an account represent arithmetic sequence.
View full solution →If for an AP if common difference is negative then it is possible that sum of first $m$ terms of AP is the sum of first $n$ terms of AP
View full solution →In an AP: $l = 28, S = 144,$ and there are total $9$ terms. Find $'a'.$
View full solution →Find the sum of the APs: $0.6, 1.7, 2.8,….,$ to $100$ terms.
View full solution →Find the sum of the APs: $–37, –33, –29, …,$ to $12$ terms.
View full solution →Find the sum of an AP given as: $2, 7, 12,...$ upto $10$ terms.
View full solution →In the AP $2, ? , 26,$ find the missing terms?
View full solution →A small terrace at a football ground comprises of $15$ steps each of which is $50$ m long and built of solid concrete.
Each step has a rise of $\frac{1}{4}$m and a tread of $\frac{1}{2}$m. (see figure). Calculate the total volume of concrete required to build the terrace.
$[$Hint: Volume of concrete required to build the first step = $\frac 14 \times \frac 12 \times 50 m^3$
View full solution →Each step has a rise of $\frac{1}{4}$m and a tread of $\frac{1}{2}$m. (see figure). Calculate the total volume of concrete required to build the terrace.
$[$Hint: Volume of concrete required to build the first step = $\frac 14 \times \frac 12 \times 50 m^3$
The houses of a row are numbered consecutively from $1$ to $49$. Show that there is a value of $x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of $x$.
$[$Hint: $S_{x-1}= S_{49}- S_x]$
View full solution →$[$Hint: $S_{x-1}= S_{49}- S_x]$
Which term of the AP: $121, 117, 113, ....$is its first negative term?
[Hint: Find n for $a_n < 0$]
View full solution →[Hint: Find n for $a_n < 0$]
Find the sum of first $51$ terms of an $AP$ whose second and third terms are $14$ and $18$ respectively.
View full solution →The first and the last terms of an $A.P$ are $17$ and $350$ respectively. If the common difference is $9$, how many terms are there and what is their sum?
View full solution →A ladder has rungs $25\ cm$ apart. The rungs decrease uniformly in length from $45\ cm$ at the bottom to $25\ cm$ at the top. If the top and bottom rungs are $2\frac 12m$ apart, what is the length of the wood required for the rungs?
$[$Hint: Number of rungs $= \frac{250}{25} + 1]$
View full solution →$[$Hint: Number of rungs $= \frac{250}{25} + 1]$
The sum of the third and the seventh terms of an $AP$ is $6$ and their product is $8.$ Find the sum of the first sixteen terms of the $AP.$
View full solution →If the sum of the first $7$ terms of an $A.P.$ is $49$ and that of the first $17$ terms is $289,$ find the sum of its first $n$ terms.
View full solution →Find the sum of first $22$ terms of an $AP$ in which $d = 7$ and $22nd$ term is $149.$
View full solution →The first term of an $AP$ is $5,$ the last term is $45$ and the sum is $400$. Find the number of terms and the common difference.
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