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Find the nth term of the geometric sequence whose first term a=3, and common ratio r=2

Sagot :

First, find the pattern of the geometric sequence:

[tex]an = a1(r) ^{n-1} [/tex]

Given a1= 3 and common ratio= 2

[tex]an = 3 (2) ^{n-1} [/tex]

Using this pattern, find the 2nd and 3rd term:
n = 2
[tex]a2 = 3(2) ^{2-1} [/tex]
[tex]a2=3(2) ^{1} [/tex]
a2 = 3(2)
a2 = 6, second term

n = 3
[tex]a3 = 3(2) ^{3-1} [/tex]
[tex]a3 = 3(2) ^{2} [/tex]
[tex]a3=3(4)[/tex]
a3 = 12, third term

Use the same pattern for the next terms of this geometric sequence.