Question

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 53n − 82

Answer 1

Given

`a_n=53n-82`

To find:

The first terms of the sequence.

Step-by-step explanation:

It is given that,

`a_n=53n-82`

That implies,

For n=1,

`\begin{gathered} a_1=53(1)-82 \\ =53-82 \\ =-29 \end{gathered}`

For n=2,

`\begin{gathered} a_2=53(2)-82 \\ =106-82 \\ =24 \end{gathered}`

For n=3,

`\begin{gathered} a_3=53(3)-82 \\ =159-82 \\ =77 \end{gathered}`

For n=4,

`\begin{gathered} a_4=53(4)-82 \\ =212-82 \\ =130 \end{gathered}`

Hence, the first four terms of the sequence is -29, 24, 77, 130.