Find the sum of the following

(iii) 6 + 13 + 20 +...........+ 97

Solution :

l = 97, a = 6, d = 13 - 6 = 7

From this, we have to find the number of terms.

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

n = [(97 - 6)/7] + 1

= (91/7) + 1

n = 13 + 1

n = 14

Sn = (n/2) [a + l]

= (14/2)[6 + 97]

= 7[103]

= 721

Hence the sum of given series is 721.