Question

Find a1 for the given geometric series.
sn=48455, r=3.2, n=3?

Answer 1

`S_n=(a_1(1-r^n))/(1-r)\\\\S_n=48455;\ r=3.2;\ n=3\\\\subtitute\\\\(a_1(1-3.2^3))/(1-3.2)=48455\\\\(a_1(1-32.768))/(-2.2)=48455\\\\(-31.768a_1)/(-2.2)=48455\\\\14.44a_1=48455\ \ \ \ |divide\ both\ sides\ by\ 14.44\\\\a_1\approx3355.61`

Answer 2

Sn = a1 ( 1 - r^n) / (1 - r)
a1=Sn(1-r) / (1 - r^n)
by putting values we get
a1 = 48455(-2.2) / (1 - (3.2^5) )
a1 = (-106601) / (-31.768)
a1 = 3355.609418
a1=3356
hope this helps