Question

PLEASE HELP A store 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.

Answer 1

Distribute 10 to (k – 1) and simplify.

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used. The upper index is 10*12=120.

The values of the summations are 58,800 + 72,600. So, the total sales is $131,400.

Explanation:

Answer 2

Answer: 131,400$

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$