Question

An = a1 + (n - 1)d

Answer 1

Answer:

The car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.

Step-by-step 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.