Question

If the first term of an ap 2 and the sum of first 5 terms is equal to one fourth of the sum of next five terms find the sum of first 30 terms

Answer 1

here is the answer in the picture above with full methodological solvation.
hope it helped...

Answer 2

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

Assumption

First term be a

Common difference be d

Hence,

a = 2

$\tt{\rightarrow S_{5} =\dfrac{1}{4}[S_{10} -S_{5}]}$

Solving it

$\tt{\rightarrow 4 S_{5}= S_{10}-S_{5}}$

$\tt{\rightarrow 5S_{5}=S_{10}}$

Now,

$\tt{\rightarrow 5\times\dfrac{5}{2}[2(2)+4d]=\dfrac{10}{2}[2(2)+9d]}$

= 5[2 + 2d] = 4 + 9d

$\tt{\rightarrow S_{30}=\dfrac{30}{2}[2(2)+29(-6)]}$

= 15[4 - 174]

= 15(-170)

= -2550