The formula for the sum of the first n terms of a geometric sequences #S_n=5^(n-1)# how do you find the first four terms of the sequence?

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Answer 1 · 2016-08-22T06:00:12

The terms are, #t_1=4/5, t_2=4, t_3=20, and, t_4=100#.

Given that, #S_n=5^(n-1)=5^n/5#.

Observe that, in any sequence #{t_n : n in NN},#

#S_n=ul(t_1+t_2+t_3+...+t_(n-1))+t_n#

#=S_(n-1)+t_n#

#rArr t_n=S_n-S_(n-1)#.

Using this Formula in our case, we get,

#t_n=5^n/5-5^(n-1)/5=5^n/5-5^n/25#

#=5^n/25(5-1)=4*5^(n-2)#

Accordingly, we have,

#t_1=4/5, t_2=4, t_3=20, and, t_4=100#.