What are the total sales over thr first six months that the store is open.

Question

Sales at a new computer store total $50,000 in the first month. They project sales to increase 10% per month. What are the total sales over thr first six months that the store is open.

Answer 1

Hey Dorothy,

 

Let's get a visual on what this is asking:

 

50,000  + ______ + ________ + ________ + ________ + _________

 

The second number in this geometric series is going to be $50,000 plus 10% interest. This is represented by:

 

50,000 (1.1) = 50,000 ( 1 + .10) = 50,000 + 5,000 = 55,000

 

So we must multiply by 1.1 each time to find the next number.

 

The formula for calculating the sum of a geometric series is:

 

S_n = a₁(1 - rⁿ) divided by (1 - r).

 

Let's confirm what we know.

 

S_{n =} the sum of the first n terms .... this is what we are trying to calculate.

a₁ = the first term = 50,000

r = the common ration (what we must multiply by each time to find the next term = 1.1

n = the number of terms = 6

 

S_n = (50,000)(1 - 1.1⁶) divided by (1 - 1.1)

 

Order of operations must be followed:

 

S_n = (50,000)(1-1.77) divided by (1- 1.1)

S_n = (50,000)(-.77) divided by (1-1.1)

S_{n =} -38,578.05 divided by (1-1.1)

S_n = -38,578.05 divided by -.1

S_n = 385,780.50

 

The total sales over the first six months the store is open is $385,780.50.

 

I hope this helps!