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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 ]Solution: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 = -41/204From (1) => 2a + 16d = 48/17=> 2a = 48/17 - 16d=> 2a = 48/17 - 16 × -41/204=> 2a = 48/17 - -164/51=> 2a = 308/51=> a = 154/51We 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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