Astore has sales of $500 in their first month. if sales increase at a rate of $10 each month, they can be modeled by this equation: an=500+(k-1)10 use summation notation to model and evaluate the sales for the first ten years. explain your steps.

131,400$

Step-by-step explanation:

The sale for first  month is $500.

The sale increases by $10 each month, as modelled by the equation:

a_k=500+(k-1)10

where, k = 1 (first month)

k = 2 (second month)

and so on.

we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)

Total sales = ∑ a_k

∑ a_k = ∑ (500+(k-1)10)

= 500k + ∑ (10k - 10)

= 500k + 10∑k - 10k

= 490k + 10∑k

= 490k + 10 {k*(k+1)/2}

= 490k + 5{k*(k+1)}

= 490k + 5k^2 + 5k

= 5k^2 + 495k

∴∑ a_k = 5k^2 + 495k

For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)

= 5*(120*120) + 495*120

= 72,000 + 59, 400

= 131,400$

answer: 16

step-by-step explanation: first you would add 6+6 which equals 12 then add 2+2 which equals 4. then add 12 + 4 which is 16.

hope this ^_^

a

step-by-step explanation: