Question

I need help on these three questions I’m so confused on how to answer them

Answer 1

Answer:

  1.  S(1) = 1; S(n) = S(n-1) +n^2

  2. see attached

  3. neither

Step-by-step explanation:

1. The first step shows 1 square, so the first part of the recursive definition is ...

  S(1) = 1

Each successive step has n^2 squares added to the number in the previous step. So, that part of the recursive definition is ...

  S(n) = S(n-1) +n^2

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2. See the attachment for a graph.

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3. The recursive relation for an arithmetic function is of the form ...

  S(n) = S(n-1) +k . . . . . for k = some constant

The recursive relation for a geometric function is of the form ...

  S(n) = k·S(n-1) . . . . . . for k = some constant

The above recursive relation is not in either of these forms, so it is neither geometric nor arithmetic.