Question

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

Answer 1

Answer:

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

Step-by-step 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 $a_2$

$a_2=a_1+1$

$a_2=5+1=6$

$6\neq 11$

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 $a_3$

$a_3=a_2+6$

$a_3=11+6=17$

$17\neq 23$

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 $a_2$

$a_2=2a_1-1$

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

$9\neq 11$

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 $a_2$

$a_2=5a_1+1$

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

$26\neq 11$

therefore

The recursive formula D not represent the sequence shown