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Given the recursive formula shown, what are the first 4 terms of the sequence? A) 5, 25, 100, 400B) 5, 14, 60, 236C) 5, 25, 125, 625D) 5, 20, 80, 320

Given the recursive formula shown what are the first 4 terms of the sequence A 5 25 100 400B 5 14 60 236C 5 25 125 625D 5 20 80 320 class=

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SOLUTION:

Step 1:

In this question, we have the following:

Step 2:

Given:

[tex]\begin{gathered} f(n)=5,\text{ if n =1,} \\ f(n)\text{ = 4 f(n-1) if n > 1} \end{gathered}[/tex][tex]\begin{gathered} f(1)\text{ = 5} \\ f(2)\text{ = 4 f(2-1) = 4 x f(1) = 4 x 5 = 20} \\ f(3)\text{ = 4f(3-1) =4 x f(2) = 4x20 = 80} \\ f(4)\text{ = 4 f(4-1)=4xf(3) = 4 x 80 = 320} \\ \text{Hence, the first 4 terms of the sequence are:} \\ 5,\text{ 20, 80 , 320 --- OPTION D} \end{gathered}[/tex]

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