Identifying and writing sequences

Write the recursive rule for the arithmetic sequence
82, 76, 70, 64, ...

• a₁=82; a_n = a_n-1-6
• a₁=64; a_n = a_n-1-6
• a₁=82; a_n = a_n-1+6
• a₁=64; a_n = a_n-1+6

Write a recursive rule for the arithmetic sequence 17, 1, -15, -31 . . .

• a_n = a_n-1 + 16
  a₁=17
• a_n = a_n-1 - 17
  a₁=17
• a_n = a_n-1 - 15
  a₁=17
• a_n = a_n-1 - 16
  a₁=17

What is the next term in the sequence?

-16, 18, 52, 86,...

Determine the answer that correctly list the first five terms of the sequence below.

 $a_1=-4;\ a_n=a_{\left(n-1\right)}-6$ 

• -4, -10, -16, -22, -28

• -4, 2, 8, 14, 20

• -4, -24, -144, -864, -5184

• -4, 0, 4, 8, 12

Given the arithmetic sequence 1, 4, 7, 10, 13 ... which of the choices below best represents the recursive form?

• f(x) = 3x - 2

• f(x) = 3x + 2

• f(1) = 1 ; f(x) = f(x-1)+ 3

• f(1) = -1 ; f(x) = f(x-1) + 3

Find the next three terms in the arithmetic sequence:

-33, -24, -15, -6, ...

• -1, 7, 15

• -5, 2, 9

• 3, 12, 21

• -65, -73, -81

The next two terms of the sequence 12, 17, 22, 27 are...

• 28 and 33
• 32 and 37
• 29 and 34
• 30 and 35

Given the sequence: 3, 12, 48, 96, 384, ...

What is the recursive formula?

• a₁ = 3 

  a_n = (4) a_n-1

• a₁ = 4 

  a_n = (3) a_n-1

• a₁ = 12 

  a_n = (9) a_n-1

• a₁ = 3 

  a_n = (-9) a_n-1

The explicit formula for a geometric sequence is $a_n=\frac{1}{8}\left(2\right)^{\left(n-1\right)}$ . What is a recursive formula for the sequence? 

•  $a_n=2\left(a_{\left(n-1\right)}\right);\ a_{1\ }=\ 8$  

•  $a_n=2\left(a_{\left(n+1\right)}\right);\ a_{1\ }=\ 8$  

•  $a_n=\frac{1}{2}\left(a_{\left(n+1\right)}\right);\ a_{1\ }=\ \frac{1}{8}$  

•  $a_n=2\left(a_{\left(n-1\right)}\right);\ a_{1\ }=\ \frac{1}{8}$