Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Answer 1

Hello there,

A restaurant has a profit of $1,300 in January. The profit will increase by $150 each month for 11 months.

What will the total profit be over the 12-month period?

Answer:  $25,500

Answer 2

Answer:  $25,500

Step-by-step explanation:

The given sequence {1300, 1300+150, ... } provides the following information:

• the first term (a₁) = 1300
• the difference (d) = 150

We can use the information above to find the explicit rule of the sequence:

$a_n=a_1+d(n-1)\\.\quad =1300+150(n-1)\\.\quad =1300+150n-150\\.\quad =1150+150n$

We can use the explicit rule to find the 12th term (a₁₂)

$a_n=1150+150n\\a_{12}=1150+150(12)\\.\quad =1150+1800\\.\quad =2950$

Next, we can input the first and last term of the sequence into the Sum formula:

$S_n=\dfrac{a_1+a_n}{2}\times n\\\\S_{12}=\dfrac{a_1+a_{12}}{2}\times 12\\\\.\quad =\dfrac{1300+2950}{2}\times 12\\\\.\quad =\dfrac{4250}{2}\times 12\\\\.\quad =2125\times 12\\\\.\quad =25,500$