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Sagot :

Answer:

4, 12, 44, and 173.

Explanation:

Given the recursion formula:

[tex]\begin{gathered} a_n=4a_{n-1}-4 \\ a_1=4,n\geqslant2 \end{gathered}[/tex]

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

[tex]\begin{gathered} a_2=4a_{2-1}-4=4a_1-4=4(4)-4=16-4=12 \\ \implies a_2=12 \end{gathered}[/tex]

Similarly:

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

Finally:

[tex]\begin{gathered} a_4=4a_{4-1}-4=4a_3-4=4(44)-4=176-4=173 \\ \implies a_4=173 \end{gathered}[/tex]

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