Q. 2 B3.5( 4 Votes )

Find the sum of each of the following arithmetic series:

34 + 32 + 30 + … + 10.

Answer :

Here, First term = 34

Common difference = d = 34 - 32 = - 2


Last term = l = 10


Now, 10 = a + (n - 1)d


10 = 34 + (n - 1)(-2)


10 - 34 = (n - 1)(-2)


- 24 = - 2n + 2


- 24 - 2 = - 2n


- 26 = - 2n


n = 13


n = 13


there are 13 terms in this Arithmetic series.


Now, Sum of these 13 terms is given by


S13 = [2(34) + (13 - 1)(-2)]


= (13/2) × [68 + (12)(-2) ]


= (13/2) × [68 - 24]


= (13/2) × [44]


= 13 × 22


= 286


Thus, sum of 23 terms of this AP is 286.


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