The first and last term of an AP are 17 and 350 respectively. If d is 9,how many terms are there and what's their sum?
Given:
The first and last term of an AP are 17 and 350 respectively.
The value of d is 9.
To find: How many terms are there and what's their sum?
Solution:
First term of AP = a =17; Last term = 350
Common difference = d = 9
Last term l = $a + (n-1)d$ = $17 + (n-1)9 = 350$
$(n - 1) = \frac{350-17}{9} = \frac{333}{9} = 37$
$n = 37 + 1 = 38$ terms. There are 38 terms in the AP
So sum of 38 terms of the AP = $\frac{n}{2} \times (a + l)$
= $\frac{38}{2} \times (17 + 350)$
= $19 \times 367$ = 6239
Therefore, the sum is 6239
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