How do you write the first five terms of the geometric sequence #a_1=2, r=3#?

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Answer 1 · 2017-02-16T14:38:08

First five terms of geometric sequence are #{2,6,18,54,162}#

In a geometric sequence if #a_1# is the first term and common ratio is #r#,

then the #n^(th)# term #a_n# is given by #a_n=a_1r^((n-1))#

Here #a_1=2# and #r=3#

hence #a_2=2xx3^((2-1))=2xx3^1=2xx3=6#,

#a_3=2xx3^((3-1))=2xx3^2=2xx9=18#,

#a_4=2xx3^((4-1))=2xx3^3=2xx27=54#,

#a_5=2xx3^((5-1))=2xx3^4=2xx81=162#.

Hence first five terms of geometric sequence are #{2,6,18,54,162}#