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Question
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
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Solution
Let S denotes the sum of first n terms of the AP.
∴ `"s"_"n" = ((3"n"^2) /2 +(5"n")/2)`
⇒ ` "s"_("n"-1) = (3("n"-1)^2)/2 + (5 ("n"-1))/2`
`= (3("n"^2 - 2"n" + 1))/2 + (5("n"-1))/2`
`=(3"n"^2 - "n"-2)/2`
∴ nth term pf the AP, an
= `"s"_"n" - "s"_("n"-1)`
= `((3"n"^2 + 5"n")/2) - ((3"n"^2 -"n"-2)/2)`
= `(6"n"+2)/2`
= 3n + 2
Putting n = 25, we get
a25 = 3 × 25 + 1 = 75 + 1 = 76
Hence, the nth term is (3n + 2) and 25th term is 76.
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