Question

Hello, does anyone know how to solve this? I keep getting it wrong on my homework, thanks!Find the first term of the sequence given by the following~n= 1, 2, 3...an = 5(3)^n-1 I attached an image to this question.

Answer 1

`5,15,45,135`

Step-by-step explanation:

Given the nth term of the required sequence expressed according to the equation:

`a_n=5(3)^(n-1)`

You need to get the first four terms of the sequence as shown:

For the first term, when n = 1

`\begin{gathered} a_1=5(3)^(1-1) \\ a_1=5(3)^0 \\ a_1=5(1) \\ a_1=5 \end{gathered}`

For the second term, when n = 2

`\begin{gathered} a_2=5(3)^(2-1) \\ a_2=5(3)^1 \\ a_2=5(3)_{} \\ a_2=15 \end{gathered}`

For the third term, when n = 3

`\begin{gathered} a_3=5(3)^(3-1) \\ a_3=5(3)^2 \\ a_3=5(9) \\ a_3=45 \end{gathered}`

For the fourth term, when n = 4

`\begin{gathered} a_4=5(3)^(4-1) \\ a_4=5(3)^3 \\ a_4=5(27) \\ a_4=135 \end{gathered}`

Therefore the first four terms of the sequence will be 5, 15, 45 and 135