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  • The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

8.   The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

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Let the sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2

S_n=\frac{a(1-r^n)}{1-r}

315=\frac{5(1-2^n)}{1-2}

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

-63=(1-2^n)

-63-1=(-2^n)

-64=(-2^n)

2^n=64

Therefore, n=6

Thus, the value of n is 6.

Last term of GP=6th term=a.r^n^-^1=5.2^5=5*32=160

The last term of GP =160

 

Posted by

seema garhwal

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