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

Hi!! THanks for coming to help!! :)

Answer 2

I like to think of it in terms of cents (instead of dollars), so the sequence is

25, 50, 75, 100, 125, ....

Answer 3

You're going to be adding up 31 of these terms

Answer 4

nth term:

an = a1 + (n-1)*d

an = 25 + (n-1)*25

an = 25 + 25n - 25

an = 25n

where n starts at n = 1

Answer 5

31st term:

an = 25n

a31 = 25*31

a31 = 775

Answer 6

So to add up the first 31 terms, use the formula

Sn = n*(a1 + an)/2

S31 = 31*(a1 + a31)/2

S31 = 31*(25 + 775)/2

S31 = 12400

This is the amount they'll have in cents. Divide by 100 to get the amount in dollars:

12400/100 = 124

So they'll have $124 at the end of May

Answer 7

The long way to do it is to list the first 31 terms:

25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775

Then add them up to get the same answer

25+50+75+100+125+150+175+200+225+250+275+300+325+350+375+400+425+450+475+500+525+550+575+600+625+650+675+700+725+750+775 = 12400

Answer 8

oh okay! Thanks!! That makes sense now :) So final answer is $124.. Thank you!! :)

Answer 9

yes it is, yw

Answer 10

why dont we multiply by 5,because each contributed

Answer 11

true, didn't see the part "EACH of them will put "

Answer 12

So the answer is $124 x 5=?? And the answer is actually $620 then???

Answer 13

yes, if each person is putting in $0.25, $0.50, ... for 31 days

Answer 14

so my final answer is actually $620?

Answer 15

yes

Answer 16

okay thanks! can u also please give @Jonask a medal for me again? haha thanks ;)