Calculate the sum of first 30 terms of the H.P. - 2,- 5,- 8,- 11....

The sum of n elements of an AP with first term a and common difference d is,

Sn = n/2 [2a + (n - 1) d]

The sum of n elements of same HP is the reciprocal of the sum of n terms of AP.

Given, progression -2,-5,-8,-11,....

First term (a) = -2

Common difference (d) = - 5 - (-2) = - 5 +2 = - 3

Then the sum of first 30 terms if the AP is

S_n = 30/2 [2 × - 2 + (30 - 1) × (-3)]

= 15 × [-  4+ 29 × (-3)]

= 15 × [- 4 - 87]

= 15 × (-91)

= - 1365

Then the sum of 30 terms of HP is =1 / (- 1365) = (- 1) / 1365

Hence, the correct option is (B).i.e (- 1) / 1365