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Question
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
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Solution
Let a be the first term and d be the common difference.
Now, a = 15
Sum of first n terms of an AP is given by,
Sn = `"n"/(2)[2"a" + ("n" - 1)"d"]`
⇒ S15 = `(15)/(2)[2"a" + (15 - 1)"d"]`
⇒ 750 = `(15)/(2)(2"a" + 14"d")`
⇒ a + 7d = 50
⇒ 15 + 7d = 50
⇒ 7d = 35
⇒ d = 5
Now, 20th term = a20
= a + 19d
= 15 + 19 × 5
= 15 + 95
= 110.
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