Respuesta :
SOLUTION
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.
[tex]A(n)=425-(n-1)30[/tex]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
[tex]\begin{gathered} A(n)=425-(n-1)30 \\ A(1)=425-(1-1)30 \\ =425-0 \\ =425 \end{gathered}[/tex]The second term will be when n =2
[tex]\begin{gathered} A(2)=425-(2-1)30 \\ =425-30 \\ =395 \end{gathered}[/tex][tex]\begin{gathered} A(n)=425-(n-1)30 \\ A(3)=425-(3-1)30 \\ =435-60 \\ =365 \end{gathered}[/tex][tex]\begin{gathered} A(n)=425-(n-1)30 \\ A(4)=425-(4-1)30 \\ =425-90 \\ =335 \end{gathered}[/tex][tex]\begin{gathered} A(n)=425-(n-1)30 \\ A(5)=425-(5-1)30 \\ =425-120 \\ =305 \end{gathered}[/tex][tex]\begin{gathered} A(n)=425-(n-1)30 \\ A(6)=425-(6-1)30 \\ =425-150 \\ =275 \end{gathered}[/tex]Hence, the first six terms are 425, 395,365,335,305,275 respectively.
