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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.

Respuesta :

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.

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