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Question

Sum of n terms of series 12+16+24+40+will be


A

22n-1+8n

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B

22n-1+6n

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C

32n-1+8n

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D

42n-1+8n

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Solution

The correct option is D

42n-1+8n


Explanation for the correct option :

Step-1 : Reforming the given series

Let S be the sum of the first n terms of the given series 12+16+24+40+

i.e. S=12+16+24+40++tn, where tn is the nth term of the series. To find tn we shall rewrite the series as follows :

12+16+24+40+=8+22+8+23+8+24+8+25+

So, using the above pattern, we get tn=8+2n.

Step-2 : Finding the value of S

We have

S=8+22+8+23+8+24+8+25++8+2n=8+8++8+22+23++2n=8n+222n-1-12-1=8n+42n-1

Here, we have used the fact that the sum of the first n terms a geometric series with the first term a and common ratio r is arn-1r-1.

Hence, option (D) is the correct answer.


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