Question

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.

• A. 2

Answer 1

The correct option is A 2
Let, 'a' be the first term and 'd' be the common difference of the AP.

$\because$ Sum of n terms of an AP is:

$\frac{n}{2}\times$(2a + (n-1)d)

$\therefore$ Sum of first 7 terms
$=\frac{7}{2}\times$(2a + (7-1)d)

$=\frac{7}{2}\times$ (2a + 6d)

$=7\times$ (a+3d)

and Sum of first 17 terms
$=\frac{17}{2}\times$(2a + (17-1)d)

$=\frac{17}{2}\times$ (2a + 16d)

$=17\times$ (a + 8d)
Given, Sum of first 7 terms = 49
and Sum of first 17 terms = 289

$\therefore$ 7 $\times$ (a+3d) = 49

$\Rightarrow$ a + 3d = 7 ......(1)

and, 17 $\times$ (a + 8d) = 289

$\Rightarrow$ a + 8d = 17.........(2)

Subtracting (1) from (2), we get
5d = 10
$\Rightarrow$ d = 2
$\therefore$ Common difference of the given AP is 2.