Class 11 • Maths • Chapter 8
SEQUENCES AND SERIES
True & False Quiz
Find the pattern. Sum the infinity.
✓True
✗False
25
Questions
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Ch.8
Chapter
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XI
Class
Why True & False for SEQUENCES AND SERIES?
How this format sharpens your conceptual clarity
🔵 Sequences and Series model growth, decay and accumulation — compound interest, population dynamics, and more.
✅ T/F distinguishes AP from GP, tests convergence of infinite GP, and checks AM≥GM — standard Board and JEE topics.
🎯 An infinite GP converges ONLY when |r|<1; for |r|≥1 the sum does not exist.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
A sequence is an ordered list of numbers defined by a definite rule.
Q 2
The \(n\)th term of an arithmetic progression (AP) is given by \(a+(n-1)d\).
Q 3
If the common difference of an AP is zero, then all its terms are equal.
Q 4
The sequence \(2,4,8,16,\ldots\) is an arithmetic progression.
Q 5
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\).
Q 6
In a geometric progression (GP), the ratio of any term to its preceding term is constant.
Q 7
The \(n\)th term of a GP with first term \(a\) and common ratio \(r\) is \(ar^n\).
Q 8
If the common ratio of a GP is \(1\), then the GP is constant.
Q 9
The sum of the first \(n\) terms of an AP depends on \(n,a,\) and \(d\).
Q 10
The sum of the first \(n\) terms of a GP always exists for all real values of \(r\).
Q 11
The arithmetic mean between two numbers \(a\) and \(b\) is \(\frac{a+b}{2}\).
Q 12
The geometric mean between two positive numbers \(a\) and \(b\) is \(\sqrt{ab}\).
Q 13
If three numbers are in AP, then the square of the middle term equals the product of the extremes.
Q 14
If three numbers are in GP, then the square of the middle term equals the product of the other two.
Q 15
The sequence defined by \(a_n=(-1)^n\) is an AP.
Q 16
The sum of the first \(n\) terms of a GP with \(|r|<1\) approaches a finite limit as \(n\to\infty\).
Q 17
The sequence of partial sums of an AP is always an AP.
Q 18
If the sum of the first \(n\) terms of an AP is linear in \(n\), then the AP has zero common difference.
Q 19
In an AP, the sum of terms equidistant from the beginning and end is constant.
Q 20
The sequence whose \(n\)th term is \(a_n=n^2\) is an arithmetic progression.
Q 21
If \(a,b,c\) are in AP and positive, then \(a^2,b^2,c^2\) are also in AP.
Q 22
If \(a,b,c\) are in GP, then \(\log a,\log b,\log c\) are in AP.
Q 23
The sum of the first \(n\) terms of an AP is maximum when the terms are symmetrically distributed about zero.
Q 24
If the \(p\)th, \(q\)th, and \(r\)th terms of an AP are in GP, then \(2q=p+r\).
Q 25
If the \(p\)th, \(q\)th, and \(r\)th terms of a GP are in AP, then \(q^2=pr\).
Key Takeaways — SEQUENCES AND SERIES
Core facts for CBSE Boards & JEE
1
AP: nth term = a+(n−1)d; Sum = n/2 × (2a+(n−1)d).
2
GP: nth term = arⁿ−¹; Sum = a(1−rⁿ)/(1−r) for r≠1.
3
Infinite GP sum = a/(1−r) valid ONLY when |r|<1.
4
AM ≥ GM ≥ HM for positive numbers — equality iff all numbers are equal.
5
AM=(a+b)/2; GM=√(ab); HM=2ab/(a+b) for two positive numbers.
6
For two positive numbers with AM=A, GM=G, HM=H: G²=AH.