Question

Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?

graph of line going through 1, 2 and 3, 4
graph of line going through 1, 1 and 3, 3
graph of line going through 1, 4 and 3, 10
graph of line going through 1, 2 and 2, 5

Answer 1

graph of line going through 1,4 and 3,10

Answer 2

The graph that represents Margo's coin collection is:

Graph of line going through (1, 4) and (3, 10).

Explanation:

It is given that:

She was given 1 coin as a gift, and she adds 3 coins per year.

Let a_n denote the amount of Money Margo had in the end of the "nth" year.

According to the given information we have:

`a_1=1+3=4`

`a_2=4+3=7\\\\a_2=a_1+3`

`a_3=10\\\\a_3=a_2+3\\\\\\a_3=a_1+3* 2`

and so on.

Hence, we get:

`a_n=a_1+3(n-1)`

Hence, we get a Arithmetic progression.

with first term as 4 and common difference as 3.

Hence, the graph is:

Graph of line going through (1, 4) and (3, 10).

( Since at n=1 we have:
`a_n=4`

and at n=3 we have:
`a_3=10` )