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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-05-SUM-01
Sum of n Terms of an AP — Assignment
Chapter: Arithmetic Progressions
Topic: Sum of First n Terms of an AP
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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 sum of $n$ terms is:
  • A.$\tfrac{n}{2}[2a+(n-1)d]$
  • B.$na$
  • C.$a+(n-1)d$
  • D.$\tfrac{n(n+1)}{2}$
2.
$S_n=\tfrac{n}{2}(a+l)$, where $l$ is the:
  • A.first term
  • B.last term
  • C.difference
  • D.mean
3.
$1+2+\dots+n=$
  • A.$n^2$
  • B.$\tfrac{n(n+1)}{2}$
  • C.$2n$
  • D.$\tfrac{n(n-1)}{2}$
4.
The sum of the first $5$ terms of $1,2,3,\dots$ is:
  • A.$10$
  • B.$15$
  • C.$20$
  • D.$25$
5.
If $S_n=3n^2+2n$, then $a_1=$
  • A.$3$
  • B.$5$
  • C.$2$
  • D.$6$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the sum of the first $10$ terms of $2,4,6,\dots$
7.
Find the sum of the first $20$ natural numbers.
8.
Find $S_{100}$ for $a=1,\ d=1$.
9.
Find the sum $5+10+\dots+50$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the sum of the first $15$ terms of $8,3,-2,\dots$
11.
Find the sum of all two-digit multiples of $3$.
12.
Find the sum of the first $12$ terms of an AP with $a=2,\ d=3$.
13.
How many terms of $3,6,9,\dots$ add up to $165$?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the sum of the first $40$ positive integers divisible by $6$.
15.
The sum of the first $n$ terms of an AP is $3n^2+5n$. Find its $n$th term and the 25th term.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\tfrac{n}{2}[2a+(n-1)d]$
  2. (B) last term
  3. (B) $\tfrac{n(n+1)}{2}$
  4. (B) $15$
  5. (B) $5$
Section B — Short Answer (2 marks)
  1. $110$.
  2. $210$.
  3. $5050$.
  4. $275$.
Section C — Short Answer (3 marks)
  1. $-405$.
  2. $1665$.
  3. $222$.
  4. $10$.
Section D — Long Answer (5 marks)
  1. $4920$.
  2. $a_n=6n+2$; $a_{25}=152$.
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