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

Answer:

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

Hence, option 'B' is true.

Step-by-step 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.