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  4. Let Sn denote the sum of the first n terms of an A.P. If S4 = 16 and S6 = -48, then S10 is equal to :

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Q. Let $S_n$ denote the sum of the first $n$ terms of an $A.P$. If $S_4 = 16$ and $S_6 = -48$, then $S_{10}$ is equal to :

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Solution:

2{2a+3d} = 16
3(2a + 5d) = -48
2a + 3d = 8
2a + 5d = -16
d = -12
$\therefore a = 22$
$S_{10}$ = 5 {44 - 9 × 12}
= -320