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Question
Sum of the first 20 terms of an AP is −240, and its first term is 7. Find its 24th term ?
Solution
First term of the A.P. (a) = 7; sum of first 20 terms = −240.
The sum of first n terms of an AP,`S_n= n/2[2a+(n-1)d]`, where a is the first term and d is the common difference.
`therefore S_n=20/2[2xx7+(20-1)d]=240`
`rArr10[14+19d]=-240`
`rArr14+19d=-24`
`rArr19d=-38`
`rArrd=-2`
Now, 24th term of the AP, `a_24=a+(24-1)d`
On putting respective values of a and d, we get
a24 + 7 + 23 × (− 2) = 7 − 46 = − 39
Hence, 24th term of the given AP is −39.
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