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4. Erin is traveling abroad this summer and would like to have a bit of spending cash while
she's overseas. She has 100 dollars already saved and she plans on saving 40 dollars a month.
(a) Fill out the table below for the amount of money she saves as a function of how many
months she has been saving.
m
m1 2 3 4
a(m) 140
(b) Give a recursive definition for the sequence a(m). Don't forget to give an initial value.

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kudzordzifrancis

Answer:

Part a)

[tex]m \to \: a(m) \\ 1 \to \: 100 \\ 2 \to \: 140 \\ 3 \to \: 180 \\ 3\to \: 220 \\ 4 \to \: 260[/tex]

Part b)

[tex]a_n=a_{n-1}+40 \\ a_1=100[/tex]

Step-by-step explanation:

Part a)

Erina already $100 saved.

This means

[tex]a_1=100[/tex]

She plans on saving 40 dollars a month.

This means that the common difference is

[tex]d = 40[/tex]

[tex]m \to \: a(m) \\ 1 \to \: 100 \\ 2 \to \: 140 \\ 3 \to \: 180 \\ 3\to \: 220 \\ 4 \to \: 260[/tex]

Part b)

The recursive formula for an arithmetic sequence is given as

[tex]a_n=a_{n-1}+d[/tex]

The common difference is d=40 and the first term is

[tex]a_1=100[/tex]

We substitute d=40 into the formula to get:

[tex]a_n=a_{n-1}+40 \\ a_1=100[/tex]

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