Question

4.

3. On the first day of summer, Jackson landed in Japan
with $7440 in his account. He plans to spend an
average of $120 each day on his tour of Asia.
a) Write recursive and explicit functions m(t) to represent
the amount money left at t days.
Recursive:
Explicit:
R

Answer 1

• recursive: a[1] = 7440; a[n+1] = a[n] -120
• explicit: a[n] = 7440 -120(n -1)

Explanation:

The sequence of amounts in Jackson's account will be ...

7440, 7320, 7200, ...

with a first value (a1) of 7440 and a common difference (d) of -120.

The recursive formula for an arithmetic sequence is ...

a[1] = a1

a[n+1] = a[n] +d

For our sequence, the recursive formula is ...

a[1] = 7440

a[n+1] = a[n] -120

__

The explicit formula for an arithmetic sequence is ...

an = a1 +d(n -1)

For our sequence, the explicit formula is ...

a[n] = 7440 -120(n -1)