Question

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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 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

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=(a_1+a_n)/(2)* n\\\\S_(12)=(a_1+a_(12))/(2)* 12\\\\.\quad =(1300+2950)/(2)* 12\\\\.\quad =(4250)/(2)* 12\\\\.\quad =2125* 12\\\\.\quad =25,500`