Question

$a_5$ and $a_{13}$ of an arithmetic progression are 16 and 28. Then first term and common difference of the A.P are ____.

• A. 10 and $\frac{3}{2}$
• B. 5 and $\frac{3}{2}$
• C. 10 and $\frac{2}{3}$
• D. 5 and $\frac{2}{3}$

Answer 1

Answer: (A)

10 and $\frac{3}{2}$

Let a and d be the first term and common difference respectively.

General term of an A.P is $a_n=a_1+(n-1)d$
Given $a_5$=16

a+(5-1)d=16
$⟹$a+4d=16--------(i)

and $a_{13}$=28
$⟹$a+12d=28--------(ii)

(ii)-(i) gives 8d=12
$⟹$ d= $\frac{3}{2}$

By substituting the value of d in (i)

we get a= 10.

$\therefore$first term=10
common difference = $\frac{3}{2}$