Question

Five 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.)

**Please explain!

Answer 1

By may 31st there Will be $620 on their fund.

Explanation:

Fund of the first day = $0.25 *5= $1.25

Fund of second day = $0.50*5= $2.5

Fund of third day = $0.75*5= $3.75

A Close observation shows there's an increase in amount to be saved by $0.25 and the total amount saved by 5 of them by $1.25.

So in the next 28 days... what will be there total.

Total = n/2(2a(n-1)d)

But where n= 31

a = 1.25

d = 1.25

Total = 31/2((2*1.25)+(31-1)1.25)

Total = 15.5(2.5+37.5)

Total= 15.5(40)

Total= 620

Answer 2

This is the arithmetic sequence, where: a 1 = 5 * 0.25 = 1.25 and d = 1.25.
( a 1 = 1.25, a 2 = 2.50, a 3 = 3.75,... )
The sum of the arithmetic sequence:
S n = n/2 ( a 1 + a n )
a n = a 1 + ( n - 1 ) d
a 31 = 1.25 + 30 * 1.25 = 1.25 + 37.50 = 38.75
S 31 = 31 / 2 * ( 1.25 + 38.75 ) =
= 31 / 2 * 40 = $620
Answer:
At the end of May, there will be $620.