Question

You borrow $425 from a friend the first week and pay the friend back $30 each week thereafter. Write the first six terms in the sequence. Explain what the sixth term means in the context of the situation.Write the first six terms in the sequence.The first term is __The second term is __The third term is __The fourth term is __The fifth term is __The sixth term is __

Answer 1

Given that the money borrowed is $425 and the amount paid back each week thereafter is $30. Let A(n) be the amount paid back after n weeks. Since $30 is paid back to my friend after each week, so (n-1)30 is returned to my friend after (n-1) weeks. Also since I borrowed $425 in the first week, so the amount to return after (n) weeks is 425-(n-1)(30). Therefore, the sequence below represents the amount left to return after n weeks.

`A(n)=425-(n-1)30`

Hence, the sixth term in the context of this situation means the amount remaining for me to pay my friend after the 6th week, i.e, n=6.

The first six terms in the sequence can be derived by using the sequence formula defined above:

The first term will be when n =1

`\begin{gathered} A(n)=425-(n-1)30 \\ A(1)=425-(1-1)30 \\ =425-0 \\ =425 \end{gathered}`

The second term will be when n =2

`\begin{gathered} A(2)=425-(2-1)30 \\ =425-30 \\ =395 \end{gathered}`
`\begin{gathered} A(n)=425-(n-1)30 \\ A(3)=425-(3-1)30 \\ =435-60 \\ =365 \end{gathered}`
`\begin{gathered} A(n)=425-(n-1)30 \\ A(4)=425-(4-1)30 \\ =425-90 \\ =335 \end{gathered}`
`\begin{gathered} A(n)=425-(n-1)30 \\ A(5)=425-(5-1)30 \\ =425-120 \\ =305 \end{gathered}`
`\begin{gathered} A(n)=425-(n-1)30 \\ A(6)=425-(6-1)30 \\ =425-150 \\ =275 \end{gathered}`

Hence, the first six terms are 425, 395,365,335,305,275 respectively.