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How many terms of AP 10,8,6 ....must be taken to give the sum of -126 |
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Answer» Answer: 18 terms will be required Step-by-step EXPLANATION: sum of AP : Sn = n/2 [2A+(n-1)d] a=10, a2=8 d = a2-a = 8-10 = -2 Sn = -126 -126 = n/2 [20+(n-1)(-2)] = n/2 (20-2n+2) from rhs taking 2 common -126 = n(10-n+1) = 11n-n^2 forming quadratic EQUATION in n : n^2 - 11n - 126 = 0 factors of (-126) to form 11 >>> (-18) and (+7) equation : n^2 -18n + 7n - 126 = 0 factorising : (n+7)(n-18) = 0 this gives n = -7 or n = +18 since n = no. of terms cannot be negative n=18 |
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