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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-05-CT
Arithmetic Progressions — Full Chapter Test
Chapter: Arithmetic Progressions
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 constant difference in an AP is the:
  • A.first term
  • B.common difference
  • C.common ratio
  • D.mean
2.
The first term is denoted by:
  • A.$d$
  • B.$a$
  • C.$n$
  • D.$l$
3.
The $n$th term of an AP is:
  • A.$a+nd$
  • B.$a+(n-1)d$
  • C.$ar^{n-1}$
  • D.$nd$
4.
The sum of $n$ terms is:
  • A.$\tfrac{n}{2}[2a+(n-1)d]$
  • B.$na$
  • C.$a+(n-1)d$
  • D.$\tfrac{n(n+1)}{2}$
5.
Sum of first $n$ odd numbers $=$
  • A.$n^2$
  • B.$n(n+1)$
  • C.$2n$
  • D.$\tfrac{n(n+1)}{2}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the common difference of $7,4,1,-2$.
7.
In $5,8,11,\dots$, identify $a$ and $d$.
8.
Find the 10th term of $2,5,8,\dots$
9.
Find the sum of the first $10$ terms of $2,4,6,\dots$
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the common difference and 5th term of $2,6,10,\dots$
11.
In the AP $7,10,13,\dots,43$, find $a,\ d$ and $n$.
12.
Find the 20th term of $3,8,13,\dots$
13.
Find the sum of the first $15$ terms of $8,3,-2,\dots$
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
For what value of $k$ are $k+9,\ 2k-1,\ 2k+7$ in AP?
15.
In an AP, $a=5$ and the 13th term is $41$. Find $d$ and the 20th term.

Answer Key

Section A — Multiple Choice Questions
  1. (B) common difference
  2. (B) $a$
  3. (B) $a+(n-1)d$
  4. (A) $\tfrac{n}{2}[2a+(n-1)d]$
  5. (A) $n^2$
Section B — Short Answer (2 marks)
  1. $-3$.
  2. $a=5,\ d=3$.
  3. $29$.
  4. $110$.
Section C — Short Answer (3 marks)
  1. $d=4$; 5th term $18$.
  2. $a=7,\ d=3,\ n=13$.
  3. $98$.
  4. $-405$.
Section D — Long Answer (5 marks)
  1. $k=18$.
  2. $d=3$; 20th term $62$.
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