The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms

A.

nth = 3

B.

nth = 4

C.

nth = 5

D.

nth = 6

Correct answer is C

nth term of a linear sequence (AP) = a+(n − 1)d

first term = 6, last term = 10 sum − 40

i.e. a = 6, l = 10, S = 40

S\(_{n}\)= n/2(2a + (n − 1)d or Sn = ÷2 (a + l)

S\(_{n}\) = n/2(a + l)

40 = n/2(6 + 10)

40 = 8n

8n = 40

8n = 40

n = 40/8

= 5

The number of terms = 5