In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1370. They start with $125 at the start of each month they plan to deposit 20% more than the previous month. Will they have enough money for their trip? If not, how much more do they need?

Step-by-step explanation:

The savings for each month is increasing by 20%. It means that it is increasing in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

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

Where

n represents the number of terms(months) in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = $125

r = 1 + 20/100 = 1.2

From March to August, it is 5 months. Thus,

n = 5 months

Therefore, the sum of the first 8

5 terms(months), S5 is

S5 = (125 × 1.2^(5) - 1)/1.2 - 1

S5 = (125 × 1.48832)/0.2

S5 = 186.04/0.2

S5 = $930.2

They won't have enough money for the trip.

The additional amount of money that they need is

1370 - 930.2 = $439.8

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation: