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For arithemetic progression f( 7 ) = 13 , S( 14 ) = 203 , then find f( 10 ) and S( 8 ).

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Your problem `->` For arithemetic progression f( 7 ) = 13 , S( 14 ) = 203 , then find f( 10 ) and S( 8 ).


We have given `f(7) = 13, S_14 = 203` and we have to find `f(10) = ?` and `S(8) = ?`

We know that, `f(n) = a + (n - 1)d`

`f(7) = 13`

`=> a + (7 - 1)d = 13`

`=> a + 6d = 13 ->(1)`


We know that, `S_n = n/2 [2a + (n - 1)d]`

`S_14 = 203`

`=> 14/2 * [2a + (14 - 1)d] = 203`

`=> 7 * [2a + 13d] = 203`

`=> 2a + 13d = 29 ->(2)`

Solving `(1)` and `(2)`, we get `a = -5` and `d = 3`


We know that, `f(n) = a + (n - 1)d`

`f(10) = -5 + (10 - 1)(3)`

`= -5 + (27)`

`= 22`

We know that, `S_n = n/2 [2a + (n - 1)d]`

`:. S_8 = 8/2 * [2(-5) + (8 - 1)(3)]`

`= 4 * [-10 + (21)]`

`= 4 * [11]`

`= 44`






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