Question

The explicit rule for a sequence is

an=48−11n .



What is the recursive rule for the sequence?




an=an−1+37,a1=11

an=an−1−11,a1=37

an=an+1−11,a1=37

an=an−1−37,a1=11

Answer 1

the rule should be a(n)=a(1)+(n-1)d
d=-11 in this case, so a(n)=a(1)-11(n-1)
a(n)=a(1)-11n+11
a(n)=a(1)+11-11n
a(1)+11=48,
a(1)=37
B is the correct answer.

Answer 2

For an explicit formula in its simplified form, we must evaluate the first two terms.

For
`a_n=48-11n`,
`a_1=48-11=37`, and
`a_2=48-22=26`. We see that the common difference is
`37-26=-11`, and
`a_1=37`, so we write,

`a_1=37, \ \ \ a_n=a(n-1)-11`.

The correct answer is B.