Question

On = a1 + (n-1)d

A gym pass costs $30 for the first month. Each month after that, the cost is $20 per month. What is the cost for Issac to
swim for 12 months?
O $258
• $250
O $368
O $350

Answer 1

The cost for Issac to swim for 12 months is $250.

Hence, option 'B' is true.

Explanation:

Given that the gym pass costs $30 for the first month, so

• a₁ = 30

Each month after that, the cost is $20 per month, so the sequence becomes

a₁, a₂, a₃, a₄, a₅, ...

30, 50, 70, 90, 110, ...

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

`50-30=20,\:\quad \:70-50=20,\:\quad \:90-70=20,\:\quad \:110-90=20`

The difference between all the adjacent terms is the same and equal to

`d=20`

now, we have

• a₁ = 30

• d = 20

so substituting a₁ = 30 and d = 20 in the nth term of the sequence

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

`a_n=20\left(n-1\right)+30`

`a_n=20n+10`

Thus, the nth term of the sequence is:

`a_n=20n+10`

Determining the cost for Issac to swim for 12 months:

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

`a_n=20n+10`

now substituting n = 12

`a_(12)=20\left(12\right)+10`

`a_(12)=240+10`

`a_(12)=250`

Therefore, the cost for Issac to swim for 12 months is $250.

Hence, option 'B' is true.