Finding which term of an AP: Class 10 practice
To find which term of an AP equals a given number, set a + (n − 1)d equal to it and solve for n. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- nth term of an AP
The idea behind finding which term of an ap
To find which term of an AP equals a given number, set a + (n − 1)d equal to it and solve for n. n must be a positive whole number; if it isn't, the number is not a term.
Step-by-step method
- Find a and d.
- Solve a + (n − 1)d = value.
- Check n is a positive integer.
Worked example 1 (Basic)
Which term of 2, 10, 18, … is 186?
- d = 8
- 2 + (n − 1)(8) = 186
- n − 1 = 23, n = 24
- Answer: 24th term
Worked example 2 (Standard)
Is 291 a term of -7, 2, 11, …?
- -7 + (n − 1)(9) = 291
- n − 1 = 298/9 (not a whole number)
- Answer: No
Worked example 3 (Challenge)
Which term of 4, -2, -8, … is -218?
- d = -6
- 4 + (n − 1)(-6) = -218
- n − 1 = 37, n = 38
- Answer: 38th term
Common mistakes and misconceptions
- Using n instead of n − 1
- Accepting a non-integer n
Practice questions
- (Basic) Which term of -2, 1, 4, … is 55?
- (Basic) Which term of -5, 3, 11, … is 187?
- (Standard) Is 161 a term of 10, 16, 22, …?
- (Standard) Is 128 a term of -5, -1, 3, …?
- (Challenge) Which term of 10, 6, 2, … is -18?
- (Challenge) Which term of 0, -8, -16, … is -240?
Answer key with full working
- Q1: d = 3 → -2 + (n − 1)(3) = 55 → n − 1 = 19, n = 20 → Answer: 20th term
- Q2: d = 8 → -5 + (n − 1)(8) = 187 → n − 1 = 24, n = 25 → Answer: 25th term
- Q3: 10 + (n − 1)(6) = 161 → n − 1 = 151/6 (not a whole number) → Answer: No
- Q4: -5 + (n − 1)(4) = 128 → n − 1 = 133/4 (not a whole number) → Answer: No
- Q5: d = -4 → 10 + (n − 1)(-4) = -18 → n − 1 = 7, n = 8 → Answer: 8th term
- Q6: d = -8 → 0 + (n − 1)(-8) = -240 → n − 1 = 30, n = 31 → Answer: 31th 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 finding which term of an ap 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.