Question

Find the sum of all 11 terms of an A.P. whose 6^th term is 30.

Answer 1

Given, 6^th term of A.P. = 30

or, a₆ = 30

or, a + (6 – 1)d = 30

or, a + 5d = 30  ...(i)

Since, Sum of n terms of A.P. is S_n = `n/2[2a + (n - 1)d]`

∴ S₁₁ = `11/2[2a + (11 - 1)d]`

= `11/2[2d + 10d]`

= `(11 xx 2)/2 [a + 5d]`

= 11 × 30  ...[From equation (i)]

= 330