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Question

How many terms of the series 12,16,20,..... must be taken to make the sum equal to 208?

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Solution

The given series is 12,16,20,.....
Let the number of terms in the series be n , such that the sum of n terms in the series is 208
The first term in the series be a=12 and the common difference be d=1612=4
The sum of n terms in the series is n2(2a+(n1)d) , given that it is equal to 208
n2(2a+(n1)d)=208
n2(24+(n1)×4)=208
n(n+5)=104=8×13
n=8
Therefore we must take 8 terms in the series in order to make their sum equal to 208

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