Question

Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started. At the end of day 2, Greg had a total of 26 quarters saved. At the end of day 5, he had a total of 35 quarters saved.
A. How many quarters does Greg start with? Show or explain your work.
B. Write an equation to model the number of quarters Greg has saved, y, after x days.
C. Using the rate at which Greg is saving, explain why he can never have exactly 100 quarters saved by the end of any given day.

Answer 1

We let 
a1 = first term
a2 = second term
a3 = third term
and so on

We are given with
a1 + a2 = 26
S5 (sum of five terms) = 35
The formula for the sum of terms is
Sn = (a1 + an) (n/2)
SO
35 = (a1 + a5) (5/2)

The formula for an arithmetic term is
an = a1 + d(n-1)
For 
a2 = a1 + d
we know that
a1 + a2 = 26

Simply for a1, a2, and d. Then use the formula to get the other items asked.