AP sum word problems: Class 10 practice
Savings that rise by a fixed amount, seats in rows, or logs in a stack form APs. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Sum of an AP
The idea behind ap sum word problems
Savings that rise by a fixed amount, seats in rows, or logs in a stack form APs. Use Sₙ = n/2[2a + (n − 1)d], or solve for n when the total is given.
Step-by-step method
- Identify a, d and n (or the total).
- Use Sₙ.
- If n is unknown, solve the quadratic and keep the positive whole value.
Worked example 1 (Basic)
A theatre has 46 seats in the first row and 6 more in each next row. How many seats in 14 rows?
- S14 = 14/2 [92 + 78]
- = 1190
- Answer: 1190
Worked example 2 (Standard)
A theatre has 34 seats in the first row and 15 more in each next row. How many seats in 9 rows?
- S9 = 9/2 [68 + 120]
- = 846
- Answer: 846
Worked example 3 (Challenge)
A person saves ₹16 in the first week and ₹14 more each week. After how many weeks will total savings be ₹520?
- n/2[2(16) + (n − 1)14] = 520
- n = 8
- Answer: 8 weeks
Common mistakes and misconceptions
- Using aₙ instead of Sₙ
- Keeping a negative or fractional n
Practice questions
- (Basic) A theatre has 26 seats in the first row and 14 more in each next row. How many seats in 12 rows?
- (Basic) A theatre has 28 seats in the first row and 19 more in each next row. How many seats in 14 rows?
- (Standard) A theatre has 29 seats in the first row and 7 more in each next row. How many seats in 18 rows?
- (Standard) A theatre has 29 seats in the first row and 3 more in each next row. How many seats in 7 rows?
- (Challenge) A person saves ₹34 in the first week and ₹19 more each week. After how many weeks will total savings be ₹489?
- (Challenge) A person saves ₹10 in the first week and ₹14 more each week. After how many weeks will total savings be ₹2584?
Answer key with full working
- Q1: S12 = 12/2 [52 + 154] → = 1236 → Answer: 1236
- Q2: S14 = 14/2 [56 + 247] → = 2121 → Answer: 2121
- Q3: S18 = 18/2 [58 + 119] → = 1593 → Answer: 1593
- Q4: S7 = 7/2 [58 + 18] → = 266 → Answer: 266
- Q5: n/2[2(34) + (n − 1)19] = 489 → n = 6 → Answer: 6 weeks
- Q6: n/2[2(10) + (n − 1)14] = 2584 → n = 19 → Answer: 19 weeks
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 sum word problems 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.