Question

Look at the sequence in the table. Which recursive formula represents the sequence shown?

Answer 1

Option B
`a_n=2a_n_-_1+1`

Explanation:

we have

`a_1=5\\a_2=11\\a_3=23\\a_4=47\\a_5=95`

Verify each recursive formula

case A) we have

`a_n=a_n_-_1+1`

For
`a_1=5`

Find the value of
`a_2`

`a_2=a_1+1`

`a_2=5+1=6`

`6\\eq 11`

therefore

The recursive formula A not represent the sequence shown

case B) we have

`a_n=2a_n_-_1+1`

For
`a_1=5`

Find the value of
`a_2`

`a_2=2a_1+1`

`a_2=2(5)+1=11` ---> is ok

For
`a_2=11`

Find the value of
`a_3`

`a_3=2a_2+1`

`a_3=2(11)+1=23` ---> is ok

For
`a_3=23`

Find the value of
`a_4`

`a_4=2a_3+1`

`a_4=2(23)+1=47` ---> is ok

For
`a_4=47`

Find the value of
`a_5`

`a_5=2a_4+1`

`a_5=2(47)+1=95` ---> is ok

therefore

The recursive formula B represent the sequence shown

case C) we have

`a_n=a_n_-_1+6`

For
`a_1=5`

Find the value of
`a_2`

`a_2=a_1+6`

`a_2=5+6=11` ---> is ok

For
`a_2=11`

Find the value of
`a_3`

`a_3=a_2+6`

`a_3=11+6=17`

`17\\eq 23`

therefore

The recursive formula C not represent the sequence shown

case D) we have

`a_n=2a_n_-_1-1`

For
`a_1=5`

Find the value of
`a_2`

`a_2=2a_1-1`

`a_2=2(5)-1=9`

`9\\eq 11`

therefore

The recursive formula D not represent the sequence shown

case E) we have

`a_n=5a_n_-_1+1`

For
`a_1=5`

Find the value of
`a_2`

`a_2=5a_1+1`

`a_2=5(5)+1=26`

`26\\eq 11`

therefore

The recursive formula D not represent the sequence shown