AP nth term and sum: Class 10 practice
In an AP each term differs from the previous by a fixed d. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Linear equations
The idea behind ap nth term and sum
In an AP each term differs from the previous by a fixed d. aₙ = a + (n − 1)d and Sₙ = n/2 [2a + (n − 1)d].
Step-by-step method
- Find a and d from the first two terms.
- Use aₙ for a term, Sₙ for a sum.
- To find n, solve aₙ = given value for n.
Worked example 1 (Basic)
Find the 24th term of the AP -3, -4, -5, …
- a = -3, d = -1
- a24 = -3 + 23 × -1 = -26
- Answer: -26
Worked example 2 (Standard)
Find the sum of the first 16 terms of -4, 1, 6, …
- a = -4, d = 5
- S = 16/2 × [2(-4) + 15(5)] = 536
- Answer: 536
Worked example 3 (Challenge)
Which term of the AP 20, 21, 22, … is 39?
- 20 + (n − 1)(1) = 39
- n − 1 = 19
- n = 20
- Answer: 20th term
Common mistakes and misconceptions
- Using n instead of (n − 1)
- Negative d written as positive
Practice questions
- (Basic) Find the 8th term of the AP -3, -4, -5, …
- (Basic) Find the 15th term of the AP 9, 11, 13, …
- (Standard) Find the sum of the first 20 terms of 5, 8, 11, …
- (Standard) Find the sum of the first 10 terms of -2, -5, -8, …
- (Challenge) Which term of the AP 9, 6, 3, … is -66?
- (Challenge) Which term of the AP 18, 26, 34, … is 202?
Answer key with full working
- Q1: a = -3, d = -1 → a8 = -3 + 7 × -1 = -10 → Answer: -10
- Q2: a = 9, d = 2 → a15 = 9 + 14 × 2 = 37 → Answer: 37
- Q3: a = 5, d = 3 → S = 20/2 × [2(5) + 19(3)] = 670 → Answer: 670
- Q4: a = -2, d = -3 → S = 10/2 × [2(-2) + 9(-3)] = -155 → Answer: -155
- Q5: 9 + (n − 1)(-3) = -66 → n − 1 = 25 → n = 26 → Answer: 26th term
- Q6: 18 + (n − 1)(8) = 202 → n − 1 = 23 → n = 24 → Answer: 24th term
Syllabus note
This skill is listed under "Arithmetic Progressions" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is ap nth term and sum in?
"Arithmetic Progressions", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.