Question

(ii) given a = 7, a1
3 = 35, find d and Sn​

Answer 1

Answer:

$\boxed{ \sf d = 7/3 \:and\: S(n) = 273}$

Step-by-step explanation:

Given that

a = 7

a13 = 35

a13 = 35 $\implies$ a + 12d = 35

∵ a = 7

a13 = 7 + 12d

35 = 7 + 12d

28 = 12d

∴ d = 28/12 = 7/3

∵ We are given with only 13 terms , Let n be 13

$S(n) = \frac{n}{2} (a+an)$

Here , On substituting the following values in S(n)

n = 13

a = 7

d = 7/3

$S(n) = \frac{13}{2} (7+ 35)$

$S(n) = \frac{13}{2} (42)$

∴ S(n) = 13×21 = $\underline{\underline{{273}}}$