Question

In an AP the first term is 2 and the sum of the first five term is one fourth of the next five terms. Show 20th term is -112.

Answer 1

2×20=-112
40=-112
-112-40
=72answer

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

$\textbf{\underline{First\;term\;be\;p}}$

$\textbf{\underline{Common\; Difference\;be\;d}}$

Hence

AP = 2 , 2 + d , 2 + 2d , 2 + 3d

$\textbf{\underline{Sum\;of\;5\;Term}}$

= 10 + 10d

$\textbf{\underline{Sum\;of\;next\;5\;Term}}$

= 10 + 35d

Situation :-

$\tt{\rightarrow 10+10d=\dfrac{1}{4}(10+35d)}$

40 + 40d = 10 + 35d

30 = -5d

$\tt{\rightarrow\dfrac{30}{-5}=d}$

d = -6

${\boxed{\sf\:{p_{20}=p+(20-1)d}}}$

= 2 + 19(-6)

= 2 - 144

= -112

$\Large{\boxed{\sf\:{Hence\;20^{th}\;term\;is\;-112}}}$