Question

"Here are some values of sequence D"

n | D(n)
1 | 13
5 | 7
7 | 4

A) "Write a recursive definition for the sequence"
B) "Write a definition for this sequence for the nth term"

Answer 1

See below

Explanation:

A) Recursive Definition

The value of each term in a sequence that starts at 13 is reduced by 1.5 for each step in the sequence.

B) Definition for nth Term

D(n) = D(1)+(n-1)(-1.5)

D(1) = 13

D(n) = 13+(n-1)(-1.5)

Examples:

D(5) = 13 + (5-1)*(-1.5)

D(5) = 13 + (4)*(-1.5)

D(5) = 13 - 6, or 7

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D(7) = 13 + (7-1)*(-1.5)

D(7) = 13 + (6)*(-1.5)

D(7) = 4