Question

An = a1 + (n - 1)d

A car travels 300 meters the first minute. Each minute after, the car travels 120 meters. If this pattern continues, what is
the distance the car travels in 15 minutes.
4320 meters
O 2000 meters
O 2085 meters
O 1980 meters

Answer 1

The car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.

Explanation:

Given that a car travels 300 meters in the first minute, so

• a₁ = 300

Each minute after, the car travels 120 meters. , so the sequence becomes

a₁, a₂, a₃, a₄, a₅, ...

300, 420, 540, 660, 780, ...

An arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

computing the differences of all the adjacent terms

`20-300=120,\:\quad \:540-420=120,\:\quad \:660-540=120,\:\quad \:780-660=120`

The difference between all the adjacent terms is the same and equal to
`d=120`

now, we have

• a₁ = 300

• d = 120

so substituting a₁ = 300 and d = 120 in the nth term of the sequence

`a_n=a_1+\left(n-1\right)d`

`a_n=120\left(n-1\right)+300`

`a_n=120n+180`

Thus, the nth term of the sequence is:

`a_n=120n+180`

Determining the distance the car travels in 15 minutes

As we have already determined the nth term of the sequence such as

`a_n=120n+180`

now substituting n = 15

`a_(15)=120\left(15\right)+180`

`a_(15)=1800+180`

`a_(15)=1980`

Therefore, the car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.