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Progression & Series - Past Year Questions

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Q1:

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of nn for which the sum of its first nn terms is closest to 100, is
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Option: 2
Correct Answer
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Q2:

The terms of a geometric progression are real and positive. If the pp-th term of the progression is qq and the qq-th term is pp, then the logarithm of the first term is
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Option: 2
Correct Answer
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Q3:

A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?
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Option: 4
Correct Answer
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Q4:

Let a1,a2,a3a_{1}, a_{2}, a_{3} be three distinct real numbers in geometric progression. If the equations a1x2+2a2x+a3=0a_{1} x ^ 2 + 2a_{2}x + a_{3} = 0 and b1x2+2b2x+b3=0b_{1} x ^ 2 + 2b_{2}x + b_{3} = 0 have a common root, then which of the following is necessarily true?
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Option: 4
Correct Answer
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Q5:

If f(n)=1+2+3+⋯+(n+1)f(n)= 1 + 2 + 3 +\cdots+(n+1) and g(n)=∑k=1k=n1f(k)g(n)= \sum_{k=1}^{k=n} \dfrac{1}{f(k)}, then the least value of nn for which g(n)g(n) exceeds the value 99100\dfrac{99}{100} is:
199
Correct Answer
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Q6:

The sum of the first 15 terms in an arithmetic progression is 200, while the sum of the next 15 terms is 350. Then the common difference is
Answer options
Option: 2
Correct Answer
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Q7:

The numbers −16,2x+3−22x−1−16,22x−1+16-16,2^{x+3}-2^{2 x-1}-16,2^{2 x-1}+16 are in an arithmetic progression. Then xx equals ________.
3
Correct Answer
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Q8:

The 3rd ,14th 3^{\text {rd }}, 14^{\text {th }} and 69th 69^{\text {th }} terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the nth n^{\text {th }} term of the arithmetic progression, then nn equals ________.
344
Correct Answer
Explanation →

Q9:

A new sequence is obtained from the sequence of positive integers (1,2,3,…)(1,2,3, \ldots) by deleting all the perfect squares. Then the 2022nd 2022^{\text {nd }} term of the new sequence is ________.
2067
Correct Answer
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Q10:

Let SnS_n be sum of the first nn terms of an A.P. If S5=S9S_5 = S_9, what is the ratio of a3:a5a_3 : a_5
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Option: 1
Correct Answer
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Q11:

The sum up to 1010 terms of the series 1⋅3+5⋅7+9⋅11+...1 \cdot 3 + 5 \cdot 7 + 9 \cdot 11 + ... is
5310
Correct Answer
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Q12:

It is given that the sequence {xnx_n} satisfies x1=0,xn+1=xn+1+2√(1+xn)x_1 = 0, x_{n+1} = x_n + 1 + 2√(1+x_n) for n=1,2,...n = 1,2,... Then x31x_{31} is _______
960
Correct Answer
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Q13:

If 112+122+132+…\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \ldots up to ∞=π26\infty = \frac{\pi^2}{6}, then the value of 112+132+152+…\frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \ldots up to ∞\infty is
Answer options
Option: 1
Correct Answer
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Q14:

There are numbers a1,a2,a3,…,ana_1, a_2, a_3, \ldots, a_n each of them being +1+1 or −1-1. If it is known that a1a2+a2a3+a3a4+…an−1an+ana1=0a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0 then
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Option: 3
Correct Answer
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Q15:

Let α,β\alpha, \beta be the roots of x2−x+p=0x^2 - x + p = 0 and γ,δ\gamma, \delta be the roots of x2−4x+q=0x^2 - 4x + q = 0 where p and q are integers. If α,β,γ,δ\alpha, \beta, \gamma, \delta are in geometric progression then p+qp + q is
Answer options
Option: 1
Correct Answer
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Q16:

If (1+x−2x2)6=A0+∑r=112Arxr(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r, then the value of A2+A4+A6+⋯+A12A_2 + A_4 + A_6 + \cdots + A_{12} is
Answer options
Option: 1
Correct Answer
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Q17:

The number of terms common to both the arithmetic progressions 2,5,8,11,...,1792, 5, 8, 11, ..., 179 and 3,5,7,9,...,1013, 5, 7, 9, ..., 101 is
Answer options
Option: 1
Correct Answer
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Q18:

Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The 6389th digit in this sequence is
4
Correct Answer
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Q19:

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :
The sum of nn terms of the Progression
1+12+122+123+1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+ is 2n−1−12n−1\frac{2^{n-1}-1}{2^{n-1}}.
Reason (R) :
Sum of a geometric series having nn terms is given by Sn=a(1−rn)1−rS_{n}=\frac{a\left(1-r^{n}\right)}{1-r}, where aa is the 1st 1^{\text {st }} term and rr is the common ratio.
Answer options
Option: 4
Correct Answer
Explanation →

Q20:

Assertion [A]: Sum of the first hundred even natural numbers divisible by 5 is 45050.
Reason (R): Sum of the first n-terms of an Arithmetic Progression is given by S=(n/2)∗(a+l)S = (n/2) *(a + l) where a=first term, l=last term.
Choose the correct answer from the options given below.
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Option: 4
Correct Answer
Explanation →

Q21:

The sum of n−n- terms of sequence 11×2+12×3+13×4……\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4} \ldots \ldots. Is
Answer options
Option: 4
Correct Answer
Explanation →

Q22:

If the mthm^{\text{th}} term of an arithmetic progression is 1n\frac{1}{n} and the nthn^{\text{th}} term is 1m\frac{1}{m}, then the mnthmn^{\text{th}} term of this progression will be
Answer options
Option: 4
Correct Answer
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Q23:

The value of (19−8−18−7+17−6−16−5+15−4)(\frac{1}{\sqrt{9}-\sqrt{8}} - \frac{1}{\sqrt{8}-\sqrt{7}} + \frac{1}{\sqrt{7}-\sqrt{6}} - \frac{1}{\sqrt{6}-\sqrt{5}} + \frac{1}{\sqrt{5}-\sqrt{4}}) is
Answer options
Option: 4
Correct Answer
Explanation →

Q24:

The height of nineteen people of comic book is in Arithmetic progression. The average height of them is 19 feet. If the tallest is 37 feet. Then what is the height of the shortest?
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Option: 2
Correct Answer
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Q25:

The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.
Answer options
Option: 1
Correct Answer
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Q26:

Given (A=265)(A = 2^{65}) and (B=264+263+262+...+20)(B = 2^{64} + 2^{63} + 2^{62} + ... + 2^0), which of the following is true?
Answer options
Option: 4
Correct Answer
Explanation →

Q27:

If log⁡2,log⁡(2x−1),log⁡(2x+3)\log 2, \log (2x - 1), \log (2x + 3) are in A.P, then xx is equal to ____
Answer options
Option: 1
Correct Answer
Explanation →

Progression & Series - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Progression & Series Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!