Question

Three friends agree to save money for a graduation road trip. They decide that each of them will put $0.25 in the fund on the first day of May, $0.50 on the second day, $0.75 on the third day, and so on. At the end of May, there will be $_____ in their fund. (Hint: There are 31 days in May.)

Answer 1

Answer: At the end of May, there will be $372.

Step-by-step explanation:

Since we have given that

On the first day of May, each one save =$0.25

Number of friends = 3

Total save on the first day of May is given by

`0.25* 3=\$0.75`

Similarly,

On the second day of May, each one save =$0.25

Total save on the second day of May is given by

`0.50* 3=\$1.5`

Similarly,

On the third day of May, each one save =$0.25

Total save on the third day of May is given by

`0.75* 3=\$2.25`

This series becomes arithmetic progression,

`0.75,1.5,2.25......`

Here, a = 0.75

d=common difference is given by

`d=a_2-a_1=1.5-0.75=0.75\\d=a_3-a_2=2.25-1.5=0.75`

Since there are 31 days in the month of May,

So, n=31

We need to calculate the sum of 31 terms to get our answer,

`S_n=(n)/(2)(2a+(n-1)d)\\\\S_(31)=(31)/(2)(2* 0.75+(31-1)* 0.75)\\\\=(31)/(2)(1.5+30* 0.75)\\\\=(31)/(2)(24)\\\\=31* 12\\\\=\$372`

Hence, at the end of May, there will be $372.