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Sum of 8 terms of series 1+5+13+29....  is

 

Option: 1

996


Option: 2

1000


Option: 3

904


Option: 4

926


Answers (1)

best_answer

Differnce of consecutive terms are

4,8,16,........ which is a GP with r = 2

So, let a_n=a.2^n+c

Put n =1 : a_1=a.2+c\Rightarrow 2a+c=1                    ........(1)

Put n = 2: a_2=a.2^2+c\Rightarrow 4a+c=5                    ...........(2)

(2) - (1) : 2a=4\Rightarrow a=2

Using (1) \Rightarrow c =-3

So, a_n=2.2^n-3

\sum a_n=2\sum 2^n-3\sum 1

              =2(2+2^2+2^3+.....2^n)-3.n

             =2.2\frac{(2^n-1)}{(2-1)}-3n

            =4(2^n-1)-3n

So, S-8=4.(2^8-1)-24=996

Posted by

vinayak

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