Class 10 • Maths • Chapter 5
Arithmetic Progressions
True & False Quiz
Common Difference. nth Term. Sum.
✓True
✗False
25
Questions
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Ch.5
Chapter
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X
Class
Why True & False for Arithmetic Progressions?
How this format sharpens your conceptual clarity
🔵 APs model uniform change — savings, salary increments, seats in rows, and stacking problems — real-life situations in Board exams.
✅ T/F tests the nth term formula, sum formula, and conditions for a sequence to be an AP.
🎯 If three numbers a, b, c are in AP, then b − a = c − b, i.e., 2b = a + c — the middle term is the AM.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
In an arithmetic progression (AP), the difference between consecutive terms is constant.
Q 2
The first term of an AP is always denoted by \(a\).
Q 3
If the common differencedddis negative, the AP is always decreasing.
Q 4
The nth term of an AP is given by \(a_n=a+(n-1)d\).
Q 5
The sum of the first n terms of an AP can be \(S_n = \frac{n}{2} [2a + (n-1)d]\).
Q 6
Every sequence of numbers is an arithmetic progression.
Q 7
In an AP with 5 terms, the middle term is the arithmetic mean of all terms.
Q 8
If three numbers in AP have sum 24 and middle term 8, they are 4, 8, 12.
Q 9
The common difference can be zero in an AP.
Q 10
The 10th term from the end of an AP with 20 terms equals the 11th term from the start.
Q 11
\(S_n = \frac{n}{2} (first\ term + last\ term)\) applies only to increasing APs.
Q 12
If the sum of first 10 terms is 100 and first term is 5, thendddmust be positive.
Q 13
In AP 3, 6, 9, ..., the 100th term exceeds 300.
Q 14
The number of terms in AP 2, 5, 8, ..., 26 is 10.
Q 15
If a, b, c are in AP, then 2b = a + c.
Q 16
The sum \(S_{2n} = 2 S_n\) for any AP.
Q 17
In AP with \(a=1,\ d=2,\ S_5 = 35\).
Q 18
An AP can have fractional common difference.
Q 19
The last term l of AP is \(a + n d\).
Q 20
If 5 terms in AP sum to 25, average term is 5.
Q 21
Sequence 1, 1, 1, 2, 2, 3, 3 is an AP.
Q 22
For AP 10, 7, 4,..., sum of first 10 terms is negative.
Q 23
\(n\)th term from end is \(l - (n-1)d\).
Q 24
\(S_n\) formula assumes positive terms only.
Q 25
If \(d=0,\ S_n = n a\).
Key Takeaways — Arithmetic Progressions
Core facts for CBSE Boards & exams
1
nth term: aₙ = a + (n−1)d, where a = first term, d = common difference.
2
Sum of n terms: Sₙ = n/2 · [2a + (n−1)d] = n/2 · (a + l), l = last term.
3
Common difference d = aₙ₊₁ − aₙ (constant for ALL consecutive pairs).
4
Three numbers in AP: take them as a−d, a, a+d for easy calculation.
5
If Sₙ is given, nth term = Sₙ − Sₙ₋₁ (for n ≥ 2).
6
Sum of first n natural numbers = n(n+1)/2.