Formula of nᵗʰ term of an A.P is:
- a+nd
- a+(n−1)d
- a+(n+1)d
- a(n−1)d
Show answer and explanation
Answer: B. a+(n−1)d
Standard AP formula: aₙ=a+(n−1)d.
FSC Mathematics: Sequences and Series, questions with answers
Practise 28 real Federal Board questions on Sequences and Series from 2023 to 2026. See the answer and explanation as soon as you answer.
28real questions
13multiple choice
5exam sessions
About Sequences and Series in FSC Mathematics
Sequences and Series is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th class), and about 6% of its real questions come from it. Tayyari Karo has 28 real questions on this chapter from 2023 to 2026; 13 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 12 easy, 11 medium, 5 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
In an arithmetic sequence, a₁=5 and a₁₅=75. What is the common difference?
- 3
- 4
- 5
- 6
Show answer and explanation
Answer: C. 5
d=(a₁₅−a₁)/14=(75−5)/14=5.
What is the first term of an infinite geometric series whose sum is 10, and common ratio 0.6?
- 4
- 5
- 6
- 7
Show answer and explanation
Answer: A. 4
a=S∞(1−r)=10×0.4=4.
In an arithmetic sequence, if a₁=3 and d=2, then 5th term is:
- 9
- 11
- 12
- 13
Show answer and explanation
Answer: B. 11
a₅=a₁+4d=3+8=11.
The last digit of 7¹⁰ is:
- 1
- 3
- 7
- 9
Show answer and explanation
Answer: D. 9
Units digit of 7ⁿ cycles 7,9,3,1 (period4); 10 mod4=2 ⇒ digit 9.
The nth term of a series 3×1² + 5×2² + 7×3² + ... is:
- (2n−1)n²
- (2n+1)(n+1)²
- (2n+1)n
- (2n+1)n²
Show answer and explanation
Answer: D. (2n+1)n²
Each term is (2n+1)·n²: check n=1: 3×1=3 ✓; n=2: 5×4=20 ✓; n=3: 7×9=63 ✓.
Find the sum of the geometric series 2/3, −1, 3/2, … up to 5 terms.
Show model answer
a=2/3, r=−1÷(2/3)=−3/2
S₅ = a(1−r⁵)/(1−r) = (2/3)(1−(−3/2)⁵)/(1−(−3/2)) = (2/3)(1+243/32)/(5/2)
= (2/3)(275/32)(2/5) = 55/24
A bouncing ball rebounds 80% of its previous height. If the ball is dropped from a height of 50 meters, find the total distance traveled by the ball before coming to rest.
Show model answer
Total distance = h + 2hr/(1−r), h=50, r=0.8
= 50 + 2(50)(0.8)/0.2 = 50+400
= 450 meters
Sessions with Sequences and Series questions
| Session | Questions |
|---|---|
| 2026 Annual | 7 |
| 2025 1st Annual | 8 |
| 2025 2nd Annual | 7 |
| 2024 Annual | 3 |
| 2023 Annual | 3 |
Common questions
What does the Sequences and Series chapter cover on this page?
28 real Federal Board (FBISE) Mathematics questions on Sequences and Series from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Conic Sections 46
- Vectors 46
- Integration 39
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Binomial Theorem 20
- Permutation/Combination/Probability 19
- Number Systems 17