How do you find #a_1# for each geometric series #S_n=381/64#, r=1/2, n=7?

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Answer 1 · 2016-12-25T01:00:47

#a_1 = 3#

We use the formula #s_n = (a(1 - r^n))/(1 - r)# to find the sum of the first n terms of a geometric series.

#381/64= (a(1 - (1/2)^7))/(1 - 1/2)#

#381/64 = (a(1 - 1/128))/(1/2)#

#381/64 = (127/128a)/(1/2)#

#381/64 = 254/128a#

#a = (381/64)/(254/128)#

#a = 3#

Hopefully this helps!