Question

if s8=34 and a=15 find s7​

Answer 1

$\mathfrak{\huge \underline{Given:}}$

$\sf S_8 = 34 \\\\\sf a=15$

$\mathfrak{\huge \underline{To ~find:}}$

$S_7=?$

From the formulae

$\boxed{S_n=\frac{n}{2}[2a+(n-1)d]}$

$\sf S_8=\frac{8}{2}(30+7d) \\\\\sf =4(30+7d) \\\\\sf$

But,

$\sf S_8 = 34 \\\\\sf so, 4(30+7d)= 34 \\\\\sf d = \frac{-43}{14}\\\\\sf </p><p></p><p>\huge \underline{\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \:\: \: \: \: \: \: \: \: \: \: \: \:} \\\\\sf Now, S_7= \frac{7}{2} (30+6d) \\\\\sf =7(15+3d) = 7[15+3(\frac{-43}{14})] \\\\\sf = 7 (\frac{210-129} {14}) \\\\\sf = \frac{81}{14} x 7 = \frac{81}{2}$