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How many terms of the sequence -2 3 8 13... will make the sum 568? |
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Answer» Given : SEQUENCE -2 3 8 13. To Find : How many terms of the sequence will make sum 568 Solution: sequence -2 3 8 13. a = - 2 d = 3 -(-2) = 5 n = term Sum = (n/2)(2a + (n -1)d) sum = 568 => (n/2)(2*(-2) + (n-1)5) = 568 => n(-4 + 5n - 5) = 1136 => n(5n - 9) = 1136 => 5n² - 9n = 1136 => 5n² - 9n - 1136 = 0 => 5n² - 80N + 71n - 1136 = 0 => 5n(n - 16) + 71(n - 16) = 0 => (n - 16)(5n + 71) = 0 => n = 16 , n = -71/5 ( which is not possible) Hence n = 16 16 terms will make sum 568 Learn More: For an AP sum of first 10 and 16 terms are 190 and 400 respectively ... If the sum of first 100 terms of an AP is -1 and the sum of the even ... |
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