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Let S(n) denote the sum of the first n t...

Let `S_(n)` denote the sum of the first n terms of an AP. If `S_(4) = 16 and S_(6) = -48`, then `S_(10)` is equal to

A

`-260`

B

`-410`

C

`-320`

D

`-380`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `S_(n)` denote the sum of the first n terms of an AP. Let first term and common difference of the AP be 'a' and 'd' respectively.
`:. S_(4) = 2[2a + 3d] = 16` (given)
`[ :' S_(n) = (n)/(2) [2a + (n-1)d]]`
`rArr 2a + 3d = 8`.. (i)
and `S_(6) = 3[2a + 5d] = -48` [given]
`rArr 2a + 5d = -16` ...(ii)
On subtracting Eq. (i) from Eq. (ii), we get
`2s = -24`
`rArr d = -12`
So, `2a = 44` [put `d = -12` in Eq. (i)]
Now, `S_(10) = 5[2a + 9d]`
`= 5[44 + 9 (-12)] = 5[44 -108]`
`5 xx (-64) = - 320`
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