If {an} is a geometric sequence with r=1/2 such that S6=65/8, what is the first term, a?

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n is supposed to be a subscript in {an} and 6 is supposed to be a subscript in S6.

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Answer 1 · 2018-04-17T04:49:16

First term is #260/63#.

Recall that in a geometric sequence of n terms, the sum is given by

#S_n = (a(1 - r^n))/(1 - r)#

#65/8 = (a(1 - (1/2)^6))/(1 - 1/2)#

#65/8 = (a(1- 1/64))/(1/2)#

#65/16 = a(63/64)#

#a = 260/63#

Hopefully this helps!