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Maths-

General

Easy

Question

The cost to rent a bike is $$$ 28 for the first day plus $$$ 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

hint Hint:

The General formula of any AP is $a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d$ .

A sequence is said to be arithmetic if the common difference is always constant.

The correct answer is: a8 = 42

Explanation:

We have given a cost of rent of bike $$$ 28 for the first day plus $$$ 2 for each day after that.

We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.

Step 1 of 2:
We have given first day cost is $$$ 28 and for each more day $$$ 2 will be charged
Here
a₁ = 28
d = 2
We know that general formula is a_n = a₁ + (n - 1)d
So,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 28 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 28 plus 2 n minus 2 end cell row cell a subscript n equals 2 n plus 26 end cell end table$
Step 2 of 2:
Now, Cost of renting for 8 days will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 2 n plus 26 end cell row cell a subscript 8 equals 2 left parenthesis 8 right parenthesis plus 26 end cell row cell a subscript 8 equals 16 plus 26 end cell row cell a subscript 8 equals 42 end cell end table$

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