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Match the APs given in column A with suitable common differences given in column B.
Arithmetic Progression | CBSE | Class 10 | Exercise 5.3 | Maths | NCERT Exemplar
Match the APs given in column A with suitable common differences given in column B.
Column A Column B
(A1) 2, – 2, – 6, –10,… (B1) 2/3
(A2) a = –18, n = 10, an = 0 (B2) – 5
(A3) a = 0, a10 = 6 (B3) 4
(A4) a2 = 13, a4 =3 (B4) – 4
(B5) 2
(B6) 1/2
(B7) 5

Solution:

(A1) AP is 2, – 2, – 6, – 10, ….

So simply the common difference

{{a}_{2}}-{{a}_{1}}~=-\text{2-2}=-4=({{B}_{3}})

(A2) Provided

The first term, a=-18

Number of terms, n=10

The last term, {{a}_{n}}~=0

Using the nth term formula

{{a}_{n\text{ }=}}~a+\left( n-1 \right)d

0=-18+\left( 10-1 \right)d

18=9d

d=2=({{B}_{5}})

(A3) Provided

The first term, a=0

The tenth term, {{a}_{10}}~=\text{ }6

Using the nth term formula

{{a}_{n\text{ }}}=~a+\left( n-1 \right)d

{{a}_{10}}~=a+9d

6=0+9d

d\text{ }=2/3=({{B}_{6}})

(A4) Let’s say that the first term be ‘a’ and the common difference be ‘d’

Provided that

{{a}_{2}}~=\text{ }13

{{a}_{4}}~=\text{ }3

{{a}_{2}}-{{a}_{4}}~=10

a+d-\left( a+3d \right)=10

d-3d=10

-2d=10

d=-5=({{B}_{1}})

i

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