Answered

IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Find the answers you need quickly and accurately with help from our knowledgeable and dedicated community members.

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 :

Mhanifaidn

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]
Semsee45idn

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.

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.