Q. 2 A4.1( 12 Votes )

Find the sum of each of the following arithmetic series:


Answer :

Here, First term = 7

Common difference = d = (21/2) - 7 = (7/2)


Last term = l = 84


Now, 84 = a + (n - 1)d


84 = 7 + (n - 1)(7/2)


84 - 7 = (n - 1)(7/2)


77 = (n - 1)(7/2)


154 = 7n - 7 (multiplying both sides by 2)


154 + 7 = 7n


7n = 161


n = 23


there are 23 terms in this Arithmetic series.


Now, Sum of these 23 terms is given by


S23 = [2(7) + (23 - 1)(7/2)]


= (23/2) × [14 + (22)(7/2) ]


= (23/2) × [14 + 77]


= (23/2) × [91]


= 2093/2


= 1046.5


Thus, sum of 23 terms of this AP is 1046.5.


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