Question

Instructions: Identify the type of sequence and write the recursive rule.

Sequence: −11,−3,5,13,…

Type: Geometric or Arithmetic?

an=an−1 - ?

a1= ?

Answer 1

`a_n=a_(n-1)+8,n\geq 1`

`a_1=-11`

Explanation:

We are given that a sequence

-11,-3,5,13,...

`a=a_1=-11`

`a_2=-3`

`a_3=5`

`a_2-a_1=-3-(-11)=-3+11=8`

`a_3-a_2=5-(-3)=5+3`

`a_3-a_2=8`

Common difference between two consecutive terms is equal.

Hence, the sequence is Arithmetic.

Common difference, d=8

`a_2=a_1+8=-3`

`a_3=a_2+8=5`

`a_4=a_3+8=13`

:

:

:

`a_n=a_(n-1)+8, n\geq 1`

`a_1=-11`