Question

Find the first three terms and stated term given the geometric sequence, with a1 as the first term. Given termsan=3^n-1, a5

Answer 1

First three terms: 1, 3 and 9

Stated term = 81

Step-by-step explanation:

Given the formula;

`a_n=3^(n-1)`

Let's go ahead and determine the first three terms of the geometric sequence.

For the 1st term;

`\begin{gathered} a_1=3^(1-1) \\ =3^0 \\ =1 \end{gathered}`

For the 2nd term;

`\begin{gathered} a_2=3^(2-1) \\ =3^1 \\ =3 \end{gathered}`

For the 3rd term;

`\begin{gathered} a_3=3^(3-1) \\ =3^2 \\ =9 \end{gathered}`

Let's now find the stated term;

`\begin{gathered} a_5=3^(5-1) \\ =3^4 \\ =81 \end{gathered}`