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For arithemetic progression S( 33 ) = 198 , then find f( 17 ).

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Your problem `->` For arithemetic progression S( 33 ) = 198 , then find f( 17 ).


We have given `S_33 = 198` and we have to find `f(17) = ?`

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

`S_33 = 33/2 [2a + (33 - 1)d] = 198`

`=> 33 [a + 16d] = 198`

`=> a + 16d = 6 ->(1)`


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

`f(17) = a + (17 - 1)d`

`=> f(17) = a + 16d`

`=> f(17) = 6` (Using (1))






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