Let Sn denote the sum of the first terms of an A.P.. If S_{4}=16 and S_{6}=-48 then S_{10} is equal to : 

 

 

  • Option 1)

    -380

  • Option 2)

    -320

  • Option 3)

    -260

  • Option 4)

    -410

 

Answers (1)

S_{4}=2\left ( 2a+3d \right )=16

S_{6}=3\left ( 2a+5d \right )=-48

\Rightarrow 2a+3d=8

      2a+5d=-16

So (2) - (1) 

d=-12                       2a-36=8\Rightarrow 2a=44

S_{10}=5\left [ 44+9x-12 \right ]

         =-320


Option 1)

-380

Option 2)

-320

Option 3)

-260

Option 4)

-410

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