Question

(a) Find the common difference of an A.P. whose first term is 5 and the number of terms is 30 and sum 1455.

(b) Find the common difference of an A.P. whose first term is 9, the number of terms is 7, and the sum is 0.

it's a optional mathematics Questions please solve him​

Answer 1

Sum = n/2[2a + (n - 1)d] where a = first term, n = number of terms and d = common difference

(a) 30/2(2 x 5 + (30 - 1) x d) = 1455
10 + 29d = 1455 / 15
29d = 97 - 10
d = 87 / 29 = 3

(b) 7/2(2 x 9 + (7 - 1)d) = 0
18 + 6d = 0
6d = -18
d = -3