Q26 of 55 Page 1

The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference in 9, how many terms are there and what is their sum?

Here, first term = a = 8


Common difference = 9


Last term = l = 350


To find: number of terms and their sum.


Let there be n terms in the AP.


Since, l = 350


∴ 350 = 8 + (n – 1)9


⇒ 350 -8 = 9n - 9


⇒ 342 = 9n - 9


⇒ 342 + 9 = 9n


⇒ 9n = 351


⇒ n = 39


Therefore number of terms = 39


Now, Sum of n terms of this arithmetic series is given by:


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


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


= [a + l]


Therefore sum of 39 terms of this arithmetic series is given by:


∴ S39 = [8 + 350]


= (39/2) × 358


= 39 × 179


∴ n = 39 and Sn = 6981


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