Find the sum of the following

(ii) 102, 97, 92,… up to 27 terms.

Solution :

Number of terms (n) = 27

First term (a) = 102

Common difference (d) = 97 - 102 = -5

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

= (27/2) [2(102) + (27 - 1)(-5)]

= (27/2) [204 + 26(-5)]

= (27/2) [204 - 130]

= (27/2) (74)

= 27 (37)

= 999

Hence the sum of 27 terms of the given series is 999.