Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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.

Sagot :

mhanifa

Answer:

  • 78125 dimes

Step-by-step explanation:

The payment for sessions makes a series

  • 5 dimes, 5*5 = 25 dimes, 25*5 = 125 dimes, ...

This series is GP with the first term of 5 and common ratio of 5.

The nth term would be

  • [tex]t_n=5*5^{n-1}[/tex]

Use the equation above and find the 7th term

  • [tex]t_7=5*5^6 = 5^7 = 78125[/tex]
semsee45

Answer:

[tex]a_7=5(5)^{6}[/tex]

78125 dimes

Step-by-step explanation:

The given scenario can be modeled as a geometric sequence.

A geometric sequence has a common ratio (multiplier) between each term, so each term is multiplied by the same number.

General form of a geometric sequence:

   [tex]a_n=ar^{n-1}[/tex]

where:

  • n is the nth term
  • a is the first term
  • r is the common ratio

Given:

  • The friend will pays 5 dimes the first time you help him.

Therefore, a = 5

Given:

  • The friend multiplies your payment by 5 for each study session.

Therefore, r = 5

Substitute these values into the formula to create an equation for the nth term.

[tex]\implies a_n=5(5)^{n-1}[/tex]

To find the number of dimes he will pay after 7 sessions, simply substitute n = 7 into the found equation:

[tex]\implies a_7=5(5)^{7-1}[/tex]

[tex]\implies a_7=5(5)^{6}[/tex]

[tex]\implies a_7=5 \cdot 15625[/tex]

[tex]\implies a_7=78125[/tex]

Therefore, the friend will pay 78125 dimes after the 7th study session.

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.