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If sum of first 6 terms of an AP is 36 a...

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256 , then find the sum of first 10 terms.

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Let the first term and common difference of A.P. be 'a' and 'd' respectively.
`S_(6)=36`
`rArr (6)/(2)[2a+(6-1)d]=36`
`rArr 2a+5d=12`
and `S_(16)=256 " " ...(1)`
`rArr (16)/(2)[2a+(16-1)]=256`
`rArr 2a+15d=32 " " ...(2)`
Subtract eq. (1) from eq. (2), we get
`{:(2a+15d=""32),(underset(-)""2aunderset(-)+5d=underset(-)""12),(bar(" "10d=20" ")):}`
`rArr d=2`
put d=2 in eq. (1), we get
`2a+5(2)=12`
`rArr 2a=2`
`rArr a=1`
Now, the sum of first 10 terms `S_(10)=(10)/(2)[2a+(10-1)d]`
`=5[2(1)+9(2)]=100`
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