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For arithemetic progression f( 5 ) = 56 , f( 8 ) = 86 then find f( 10 ) and S( 10 ).

Solution:
Your problem `->` For arithemetic progression f( 5 ) = 56 , f( 8 ) = 86 then find f( 10 ) and S( 10 ).


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

`f(5) = 56`

`=> a + (5 - 1)d = 56`

`=> a + 4d = 56 ->(1)`


`f(8) = 86`

`=> a + (8 - 1)d = 86`

`=> a + 7d = 86 ->(2)`

Solving `(1)` and `(2)`, we get `a = 16` and `d = 10`


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

`f(10) = 16 + (10 - 1)(10)`

`= 16 + (90)`

`= 106`

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

`:. S_10 = 10/2 * [2(16) + (10 - 1)(10)]`

`= 5 * [32 + (90)]`

`= 5 * [122]`

`= 610`






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