Question

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. Whose first term is -30 and common difference is 8. Fnd n.

Answer 1

$a_1$ = 8 $a_2$ = -30
$d_1$ = 20 $d_2$ = 8

$S_{n_1}=2S_{2n_2}$

$\frac{n}{2}(2a_1+(n-1\left)d_1\right)$ = $\frac{2n}{2}(2a_2+(2n-1\left)d_2\right)$

$\Rightarrow$16+(n-1)20 = 2 [ (-60 + (2n-1) 8)]

$\Rightarrow$16 + 20n -20 = -120 + 32n -16

$\Rightarrow$ 12n = 132

$\Rightarrow$ n = 11