Arithmetic & Geometric Progression Questions with Solutions

42 questions13 easy21 medium8 hard

An arithmetic progression (AP) is a sequence where each term differs from the previous one by a constant amount, the common difference. A geometric progression (GP) is a sequence where each term is the previous one multiplied by a constant, the common ratio. This topic covers the nth term and sum of n terms of an AP and GP, the sum of an infinite GP, arithmetic and geometric means, and word problems. Key formulas are the AP nth term a + (n - 1)d, the AP sum n/2 [2a + (n - 1)d], the GP nth term ar^(n-1), and the infinite GP sum a/(1 - r) for |r| < 1. A useful trick is to choose symmetric terms, such as a - d, a, a + d for three terms of an AP, which simplifies many questions. Practise the AP and GP questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
The arithmetic mean of two numbers a and b is 5, and the harmonic mean is 3.2. Find the numbers a and b.
A. a = 3, b = 7B. a = 4, b = 6C. a = 1, b = 9D. a = 2, b = 8
easyAsked in NIMCET 2026View solution ›
Q2.
Consider the sequence 72, 69, 66, … The numbers continue in the same pattern as long as they remain positive. What will be the maximum possible sum of the terms of this sequence?
A. 900B. 897C. 882D. 903
easyAsked in NIMCET 2026View solution ›
Q3.
If the angles of a triangle are in Arithmetic Progression, then the measures of one of the angles in radians is
A. $\frac{π}{6}$ B. $\frac{π}{3}$ C. $\frac{π}{2}$ D. $\frac{2 π}{3}$
easyAsked in MAH MCA CET 2024View solution ›
Q4.
The sum of integers between 200 and 400 that are multiples of 7 is
A. 8729B. 8700C. 8972D. 8279
easyAsked in NIMCET 2013View solution ›
Q5.
Sum of 20 terms of the series $- 1^{2} + 2^{2} - 3^{2} + 4^{2} - \dots$ is
A. 180B. 200C. 210D. 220
easyAsked in NIMCET 2013View solution ›
Q6.
If $H$ is the harmonic mean between $P$ and $Q$ , then $\frac{H}{P} + \frac{H}{Q}$ is
A. 2B. $\frac{P + Q}{Q}$ C. $\frac{P Q}{P + Q}$ D. None of these
easyAsked in NIMCET 2012View solution ›
Q7.
The sum $11^{2} + 12^{2} + 13^{2} + \dots + 30^{2}$ is
A. $9070$ B. $\frac{2}{82}$ C. $1080$ D. $9700$
easyAsked in NIMCET 2011View solution ›
Q8.
From a height of $16$ metres a ball fell down and each time it bounces half the distance back. What is the total distance travelled?
A. $45$ mB. $\infty$ C. $48$ mD. $24$ m
easyAsked in NIMCET 2008View solution ›
Q9.
An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Then what is the common difference?
A. $\frac{3}{4}$ B. $\frac{1}{2}$ C. $\frac{1}{4}$ D. $\frac{4}{3}$
easyAsked in NIMCET 2020View solution ›
Q10.
The four geometric means between 2 and 64 are
A. $\frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}$ B. $4, 8, 16, 32$ C. $42, 8, 162, 32$ D. None of the above
easyAsked in NIMCET 2021View solution ›
Q11.
Which term of the series $\frac{5}{3}, \frac{5}{4}, \frac{1}{5}, \dots$ is $\frac{5}{13}$ ?
A. 12B. 11C. 10D. 9
easyAsked in NIMCET 2022View solution ›
Q12.
The sum to infinity of a geometric progression is twice the sum of its first two terms. What are the possible values of the common ratio?
A. $\pm \frac{1}{2}$ B. $\pm \frac{1}{2}$ C. $\pm \frac{1}{3}$ D. $\pm \frac{1}{3}$
easyAsked in NIMCET 2018View solution ›
Q13.
If $x$ , $2 x + 2$ , $3 x + 3$ are the first three terms of a geometric progression, then the 4th term of the geometric progression is:
A. -13.5B. 13.5C. -27D. 27
easyAsked in NIMCET 2019View solution ›