Q6 of 67 Page 74

The first and the last terms of an arithmetic progression are 17 and 350 respectively. If the common difference is 9 then what is the number of terms in the arithmetic progression and what is their sum?

Here first term is 17 and common difference is 9
Last term l = 350


Let no. of terms be n.
Since, an = a + (n - 1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



⇒ 350 = 17 + (n - 1) × 9
⇒ 333 = (n - 1) × 9
⇒ 37 = n – 1
⇒ n = 38


Since the sum of n terms is
Sn =
So sum of 38 terms S38
= 19 [34 + 37 × 9]
= 19 × 367
= 6973


Hence, Number of terms is 38 and Sum is 6973.


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