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What is the sum of the geometric sequence 2, 10, 50, … if there are 8 terms?

1 Answer

Feb 4, 2016

#195312#

Explanation:

Since the sequence is geometric, there is a constant ratio given by #r=x_(n+1)/x_n=10/2=50/10=5#

The first term is #a=2#.

The formula for the sum to n terms of such a geometric series is given by :

#sum_(k=1)^n ar^(k-1)=(a(1-r^n))/(1-r)#

So in this particular case it becomes

#sum_(n=1)^8 2*(5)^(n-1)=(2(1-5^8))/(1-5)=195312#.

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