Question

A bus begins its trip with R occupants (including the driver). At each of the 20 stops, 3 people get on and no one leaves. If there are 3 times as many bus occupants at the end of the 20th stop as there are at the end of the 4th stop, how many occupants did the bus have immediately after the 10th stop?
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Answer 1

Using an arithmetic sequence, it is found that the bus had 42 occupants immediately after the 10th stop.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

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

In which $a_1$ is the first term.

As a function of the mth term, the nth term is given by:

$a_n = a_m + (n - m)d$

At each of the 20 stops, 3 people get on and no one leaves, hence the common difference is given by:

d = 3.

There are 3 times as many bus occupants at the end of the 20th stop as there are at the end of the 4th stop, hence:

$a_{20} = 3a_4$

We consider that:

$a_{20} = a_{4} + 16d$

$a_{20} = a_4 + 48$

Then:

$3a_4 = a_4 + 48$

$2a_4 = 48$

$a_4 = 24$

At the 10th stop, the number of occupants is given as follows:

$a_{10} = a_4 + 6d = 24 + 6(3) = 42$

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

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