Question

in an ap of first term is 2 the sum of the first five terms is one fourth of the sum of first 25 terms find the sum of first 20 terms​

Answer 1

a = 2

S5 = 1/4 S25

S20 = ?

d = x

$\frac{5}{2} (2(2) + (5 - 1)x = \frac{1}{4} \times \frac{25}{2} (2(2) + (25 - 1)x$

$\frac{5}{2} (4 + 4x) = \frac{25}{8}(4 + 24x$

$4 + 4x = \frac{5}{4} (4 + 24x)$

$16 + 16x = 20 + 120x$

$114x = - 4$

$x = \frac{ - 2}{57}$

d = -2/57

S20 = ?

$= \frac{20}{2} (2(2) + (20 - 1) \frac{ - 2}{57}$

$10(4 + 19( \frac{ - 2}{57} )$

$10(4 + \frac{ - 2}{3} )$

$10( \frac{10}{3} )$Answer = 100/3