Vidaara.orgClass 10 · Mathematics
CodeVID-M10-05-CMP-01
Components of an AP — Assignment
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 first term is denoted by:
- A.$d$
- B.$a$
- C.$n$
- D.$l$
2.
The common difference is denoted by:
- A.$a$
- B.$d$
- C.$n$
- D.$S$
3.
The $n$th term is denoted by:
- A.$a_n$
- B.$d$
- C.$S_n$
- D.$r$
4.
If $a=2,\ d=3$, the 2nd term is:
- A.$3$
- B.$5$
- C.$6$
- D.$8$
5.
The last term of a finite AP is often denoted by:
- A.$a$
- B.$d$
- C.$l$
- D.$n$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
In $5,8,11,\dots$, identify $a$ and $d$.
7.
If $a=10$ and $d=-2$, write the first three terms.
8.
Find the number of terms in $2,4,6,\dots,20$.
9.
If $a=1,\ l=19,\ d=2$, find $n$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
In the AP $7,10,13,\dots,43$, find $a,\ d$ and $n$.
11.
If $a=3,\ d=5$, find the 4th and 6th terms.
12.
The 3rd term of an AP is $12$ and $d=2$; find $a$.
13.
Find the number of terms in $6,9,12,\dots,60$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
In an AP, $a=5$ and the 13th term is $41$. Find $d$ and the 20th term.
15.
The 4th term of an AP is $0$. Show that its 25th term is three times its 11th term.
Answer Key
Section A — Multiple Choice Questions
- (B) $a$
- (B) $d$
- (A) $a_n$
- (B) $5$
- (C) $l$
Section B — Short Answer (2 marks)
- $a=5,\ d=3$.
- $10,8,6$.
- $10$.
- $10$.
Section C — Short Answer (3 marks)
- $a=7,\ d=3,\ n=13$.
- $18$ and $28$.
- $a=8$.
- $19$.
Section D — Long Answer (5 marks)
- $d=3$; 20th term $62$.
- With $a=-3d$: $a_{25}=21d=3(7d)=3a_{11}$.
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