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प्रश्न
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
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उत्तर
Here, the sum of first n terms is given by the expression,
S_n = `(3n^2)/2 + 13/2 n`
We need to find the 25th term of the A.P.
So we know that the nthterm of an A.P. is given by,
`a_n = S_n- S_(n - 1)`
So `a_25 = S_25 - S_24` ....(1)
So, using the expression given for the sum of n terms, we find the sum of 25 terms (S25) and the sum of 24 terms (S24). We get,
`S_25 = (3(25)^2)/2 + 13/2 (25)`
`= (3(25)^2)/2 + 13/2 (25)`
`= (3(625))/2 + (13(25))/2`
`= 1875/2 = 325/2`
= 2200/2
= 1100
Similarly
`S_24 = (3(24)^2)/2 + 13/2 (24)`
`= (3(576))/2 + (13(24))/2`
`= 1728/2 + 312/2`
`= 2040/2`
=1020
Now, using the above values in (1),
`a_25 = S_25 - S_24`
= 1100 - 1020
= 80
Therefore `a_25 = 80`
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