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Question

The number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30 and the last term exceeds the first by 10.5, then the number of terms in the series is

A
8
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B
4
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C
6`
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D
10
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Solution

The correct option is A 8
Let the total number of terms be '2n', first term be 'a' and common difference be 'd'
a+(2n1)d=l
and la=10.5.......................(1)
if we take only odd terms, it will also be a A.P of n terms with common difference '2d'
24=n2{2a+(n1)2d}
24=n{a+(n1)d}................(2)
Similarly,
30=n2{2(a+d)+(n1)2d}
30=n2{2a+2nd}
30=n{a+nd}........................(3)
Putting value of n{a+nd}from eq (3) to eq (2)
24=30nd
nd=6
putting value of nd in eq(1)
12d=10.5
d=1.5
So,
n=61.5=4
So, number of terms will be 2n=8
















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