Lucy's lemonade stand has increasing profits each week during the hot summer months. Lucy
finds that each week during the summer her profits increase by 10% over what they were the
previous week. In her first week of business, her profits were $50.
How much money will she make in all over 4 weeks?

she will make $232.05 in 4 weeks.

Step-by-step explanation:

Since her profit is increasing by 10% each week, then the rate at which it is increasing is in geometric progression. The common ratio, r would be 110/100 = 1.1

We would apply the formula for determining the sum of n terms of a geometric progression which is expressed as

Sn = a(r^n - 1)/(r - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms(number of weeks)

From the information given,

a = 50

r = 1.1

n = 4 weeks

Therefore,

S4 = 50(1.1^4 - 1)/(1.1 - 1)

S4 = 50(1.1^4 - 1)/0.1

S4 = $232.05

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