Question

3. The following sequence shows the number of pushups Kendall did each week, starting with her first week of exercising: 6, 18, 54, 162…
(a) What is the recursive rule for the sequence?
(b) What is the iterative rule for the sequence?

Answer 1

{{{ THE BOLDED CHARACTERS SHOULD BE SMALL. }}}

SEQUENCE: 6, 18, 54, 162

18/6 = 3

54/18 = 3

162/54 = 3

then, r (common ratio) = 3

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RECURSIVE RULE: r = 3

an = a(n - 1) × r       [formula]

ANSWER: an = a(n - 1) × 3

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ITERIATIVE RULE: r = 3, a1 = 6

an = a1 × r^(n - 1)       [formula] [ ^(n-1) is an exponent]

ANSWER: an = 6 × 3^(n - 1)