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Arithmetic Progressions
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01/06/2021 12:01 pm
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The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
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01/06/2021 12:03 pm
Given that,
First term, a = 17
Last term, l = 350
Common difference, d = 9
Let there be n terms in the A.P., thus the formula for last term can be written as;
l = a+(n −1)d
350 = 17+(n −1)9
333 = (n−1)9
(n−1) = 37
n = 38
Sn = n/2 (a+l)
S38 = 13/2 (17+350)
= 19×367
= 6973
Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.