Question

After a gas-filled balloon is released, it rises 90 feet by the end of the first minute. By the end of the second minute, the balloon rises 120 feet, and by the end of the third minute, it rises 150 feet. How many feet would the balloon rise in 8 minutes?

Answer 1

`\boxed{\text{300 ft}}`

Explanation:

You have an arithmetic sequence in which

a₁ = 90

a₂ = 120

a₃ = 150

1. Calculate the explicit formula

This is an arithmetic sequence, because there is a constant difference of 30 between consecutive terms.

The explicit formula for the nth term of an arithmetic sequence is

aₙ = a₁ + d(n - 1 )

a₁ is the first term, and d is the difference in value between consecutive terms. Thus,

aₙ = 90 + 30(n - 1) = 90 + 30n - 30

aₙ = 30n + 60

2. Calculate the eighth term

a₈ = 30 × 8 + 60 = 240 + 60 = 300

`\text{In 8 min, the balloon rises }\boxed{\textbf{300 ft}}`

Answer 2

Answer: 300 feet

Explanation:

Note that:

`120-90 = 30`

`150-120 = 30`.

Then the balloon rises at a constant rate of 30 meters per minute.

We can represent this situation through an arithmetic sequence as shown below

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

Where
`a_1=90` is the first term of the sequence and
`a_n` is the n-th term of the sequence and
`d=30` is the common difference between two consecutive terms.

In this case we look for the height of the balloon after 8 minutes.

Then we look for
`a_8`

`a_8 = 90 + 30(8-1)`

`a_8 = 90 + 30(7)`

`a_8 = 300`