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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-08-CT
Sequences and Series — Full Chapter Test
Chapter: Sequences and Series
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The $n$th term of an AP is:
  • A.$a+nd$
  • B.$a+(n-1)d$
  • C.$ar^{n-1}$
  • D.$nd$
2.
The $n$th term of a GP is:
  • A.$a+(n-1)d$
  • B.$ar^{n-1}$
  • C.$ar^n$
  • D.$nr$
3.
$\displaystyle\sum_{k=1}^{n} k=$
  • A.$n^2$
  • B.$\tfrac{n(n+1)}{2}$
  • C.$\tfrac{n(n+1)(2n+1)}{6}$
  • D.$n!$
4.
The common difference of $3,7,11,\dots$ is:
  • A.$3$
  • B.$4$
  • C.$7$
  • D.$1$
5.
The common ratio of $3,6,12,\dots$ is:
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$6$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the $15$th term of the AP $2,5,8,\dots$
7.
Find the $5$th term of the GP $3,6,12,\dots$
8.
Find $1+2+\dots+50$.
9.
Find the sum of the first $20$ natural numbers.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the sum of the first $10$ terms of the AP $2,5,8,\dots$
11.
Find the sum of the first $6$ terms of the GP $2,6,18,\dots$
12.
Find $1^2+2^2+\dots+15^2$.
13.
Which term of the AP $5,8,11,\dots$ is $50$?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The sum of three numbers in AP is $27$ and their product is $405$. Find the numbers.
15.
The sum of three numbers in GP is $13$ and their product is $27$. Find the numbers.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $a+(n-1)d$
  2. (B) $ar^{n-1}$
  3. (B) $\tfrac{n(n+1)}{2}$
  4. (B) $4$
  5. (B) $2$
Section B — Short Answer (2 marks)
  1. $44$.
  2. $48$.
  3. $1275$.
  4. $210$.
Section C — Short Answer (3 marks)
  1. $155$.
  2. $728$.
  3. $1240$.
  4. The $16$th term.
Section D — Long Answer (5 marks)
  1. $3,9,15$.
  2. $1,3,9$.
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