Question

Consider an arithmetic sequence whose sum of first 9 terms is 261 and sum of next 6 terms is 444. find the first term and common difference.

Answer 1

Let first term = a, common difference = b,

t1 = a , t9 = a + (9–1)*b = a + 8b , according to condition , a+a+8b = 24…..(1),

When we find the sum of first nine terms , we have first term is a , and last term l = a+8b, number of total terms , n= 9,

S = n/2*{a+l} = 9/2*{a +a+8b}. Now putting a+a+8b = 24 from equation (1)

S = (9/2)*24 =108