JEE MAIN - Mathematics (2019 - 12th April Morning Slot - No. 11)
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 :
- 320
- 380
- 460
- 210
Explanation
S4 = $${4 \over 2}\left( {2a + 3d} \right) = 16$$
$$ \Rightarrow 2a + 3d = 8$$
S4 = $${6 \over 2}\left( {2a + 5d} \right) = -48$$
$$ \Rightarrow 2a + 5d = -16$$
$$ \therefore $$ d = -12 and a = 22, Now S10 = $${{10} \over 2}\left( {44 - 108} \right) = - 320$$
$$ \Rightarrow 2a + 3d = 8$$
S4 = $${6 \over 2}\left( {2a + 5d} \right) = -48$$
$$ \Rightarrow 2a + 5d = -16$$
$$ \therefore $$ d = -12 and a = 22, Now S10 = $${{10} \over 2}\left( {44 - 108} \right) = - 320$$
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