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How many terms of the arithmetic sequence 5,7.9to get 140?must be added |
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Answer» For Airthmetic sequence sum of n termsSn = n/2(2a + (n-1)d) For given sequencea = 5, d = 7-5 = 2 Let sum of given m terms is 140Then,140 = m/2(2*5 + (m- 1)2)280 = m (10 + 2m - 2)2m^2 + 8m - 280 = 02m^2 + 28m - 20m - 280 = 02m(m + 14) - 20(m + 14) = 0(2m - 20)(m + 14) = 0m = 10, - 14 As number of terms cannot be negative then m = 10 Thus sum of 10 terms of given sequence is 140 that means more 7 terms need to be added. |
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