Question

Your friend asks you to help him study and will pay you 5

dimes the first time you help him. You agree to help if he
multiplies your payment by 5 for each study session. After 2
study sessions, you will receive 25 dimes, and after 3 study
sessions, you will receive 125 dimes.
Complete and solve the equation that finds the number of
dimes he will pay you after the 7th study session.
*+
*
CLEAR
= number of dimes for 7th study session
Payment for the 7th study session =
dimes

Answer 1

first part: 5^7

second part: 78125

Explanation:

Answer 2

My payment for the 7th study session will be 78125 dimes.

Explanation:

My friend will pay me 5 dimes for helping him study for the first time.

Now, I agree to help him if he multiplies my payment by 5 for each study session.

So, he will pay 25 dimes for the 2nd study session, 125 dimes for the 3rd study session and so on.

Hence, my payment in each study session increases in geometric progression as follows:

5, 25, 125, ........ so on.

So, the 7th term of this series indicates the number of dimes that my friend pays me after the 7th study session.

This is a G.P. series having first term 5 and common ratio 5, then the 7th term will be
`5* 5^((7 - 1)) = 5^(7) = 78125`

Therefore, my payment for the 7th study session will be 78125 dimes. (Answer)