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Problem: For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of first 41 terms. [ Calculator, Method and examples ]

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Your problem `->` For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of first 41 terms.


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

`S_17 = 17/2 * [2a + (17 - 1)d] = 24`

`=> 17/2 * [2a + 16d] = 24`

`=> 2a + 16 d = 48/17 ->(1)`


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

`S_24 = 24/2 * [2a + (24 - 1)d] = 17`

`=> 24/2 * [a + 23d] = 17`

`=> 2a + 23d = 17/12 ->(2)`

Solving `7 d = -287/204`

`=> d = -41/204`

From `(1) => 2a + 16d = 48/17`

`=> 2a = 48/17 - 16d`

`=> 2a = 48/17 - 16 × -41/204`

`=> 2a = 48/17 - -164/51`

`=> 2a = 308/51`

`=> a = 154/51`

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

`:. S_41 = 41/2 * [2(154/51) + (41 - 1)(-41/204)]`

`= 41/2 * [308/51 + (-410/51)]`

`= 41/2 × -2`

`= -41`






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