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Vidaara.orgClass 8 · Mathematics
CodeVID-M8-07-CT
Patterns & Sequences — Full Chapter Test
Chapter: Patterns & Sequences
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 next term of $2, 4, 6, 8, \ldots$ is:
  • A.$9$
  • B.$10$
  • C.$12$
  • D.$16$
2.
In an AP the common difference is:
  • A.changing
  • B.constant
  • C.a ratio
  • D.zero always
3.
In a GP each term is multiplied by a constant:
  • A.difference
  • B.ratio
  • C.sum
  • D.square
4.
$1, 4, 9, 16$ are:
  • A.even numbers
  • B.perfect squares
  • C.primes
  • D.cubes
5.
The $n$-th term of an AP is:
  • A.$a+nd$
  • B.$a+(n-1)d$
  • C.$ar^{n-1}$
  • D.$an$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write the next two terms: $3, 6, 9, \ldots$
7.
Find $d$ for $4, 9, 14$.
8.
Find $r$ for $4, 12, 36$.
9.
Write the next term: $1, 4, 9, 16, \ldots$
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the next two terms: $1, 1, 2, 3, 5, 8, \ldots$
11.
Find the 10th term of the AP $3, 7, 11, \ldots$
12.
Find the 5th term of the GP $3, 6, 12, \ldots$
13.
Find the missing term: $4, 9, \,\rule{1em}{0.4pt}\,, 25, 36$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
For the triangular numbers $1, 3, 6, 10, 15, \ldots$, find the next two terms and state the rule.
15.
For the AP $7, 12, 17, \ldots$, find the 15th term and the sum of the first $15$ terms.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $10$
  2. (B) constant
  3. (B) ratio
  4. (B) perfect squares
  5. (B) $a+(n-1)d$
Section B — Short Answer (2 marks)
  1. $12,\ 15$.
  2. $5$.
  3. $3$.
  4. $25$.
Section C — Short Answer (3 marks)
  1. $13,\ 21$ (Fibonacci).
  2. $39$.
  3. $48$.
  4. $16$.
Section D — Long Answer (5 marks)
  1. $21,\ 28$; add one more each time (add $6$, then $7$).
  2. $t_{15}=77$; $S_{15}=630$.
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