Question

Hello,Can you help me with the question in the photo?Thank you,

Answer 1

4, 12, 44, and 173.

Explanation:

Given the recursion formula:

`\begin{gathered} a_n=4a_(n-1)-4 \\ a_1=4,n\geqslant2 \end{gathered}`

We want to find the first four terms of the sequence.

`\begin{gathered} a_2=4a_(2-1)-4=4a_1-4=4(4)-4=16-4=12 \\ \implies a_2=12 \end{gathered}`

Similarly:

`\begin{gathered} a_3=4a_(3-1)-4=4a_2-4=4(12)-4=48-4=44 \\ \implies a_3=44 \end{gathered}`

Finally:

`\begin{gathered} a_4=4a_(4-1)-4=4a_3-4=4(44)-4=176-4=173 \\ \implies a_4=173 \end{gathered}`

The first four terms of the sequence are 4, 12, 44, and 173.