Question

The sum of first 6 terms of an ap is 36 and that of the first 16 terms is 256 then find the sum of first 10 terms

Answer 1

THEREFORE, S10 = 100

-----------------------------------------------------------------

Please mark as BRAINLIEST

Answer 2

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

Assumption

First term be a

Common difference be d

So,

$\tt{\rightarrow S_{6}=36}$

$\tt{\rightarrow S_{16}=256}$

Condition

$\tt{\rightarrow S_{6}=\dfrac{6}{2}[2a+5d]=36}$

2a + 5d = 12 ...... (1)

$\tt{\rightarrow S_{16}=\dfrac{16}{2}[2a+15d]=256}$

2a + 15d = 32 ...... (2)

Subtracting (1) from (2)

10d = 20

$\tt{\rightarrow d=\dfrac{10}{2}}$

d = 2

${\boxed{\sf\:{Substitute\;the\;value\;in\;(1)}}}$

2a + 5(2) = 12

2a + 10 = 12

2a = 12 - 10

2a = 2

$\tt{\rightarrow a=\dfrac{2}{2}}$

a = 1

Hence,

$\tt{\rightarrow S_{10}=\dfrac{10}{2}[2(1)+9(2)]}$

= 5 × (2 + 18)

= 5 × 20

= 100