Practice Explicit and Recursive Sequences

An arithmetic sequence is given below.

2, 9, 16, 23, ...

Which is the explicit formula for the n^th term a_n?

(Look at the choices carefully! You may have to simplify your equation to get the correct choice!)

• a_n = -7n+9

• a_n = 7n-5

• a_n = 7n-9

• a_n = -7n+5

Write a recursive formula for the following sequence: 10, 5, 0, -5,...

• a₁= 10

  a_n= a_n-1 - 5

• a₁= 10

  a_n= a_n-1 + 5

• a₁= 10

  a_n= a_n (5)

• a₁= 10

  a_n= a_n-1 (5)

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1 - 1

• 14

• 13

• 17

• 16

Given the recursive formula, find the explicit form
a_n = a_n-1 - 5
a₁ = 22

• a_n = 22 + (n-1)(-5)

• a_n = 22 + (n-1)(5)

• a_n = -5 + (n-1)(22)

• a_n = -16 + (n-1)(-5)

Which of the following recursive equations describe the sequence shown in the graph?

•   a_n = 5n -2

  a₁ = 2

•  a_n = 2(5)ⁿ

  a₁ = 2

•  a_{n =} a_{n-1 *} 2

  a_{1 = 2}

• a_n = a_n-1 * 5

  a₁ = 2

A formula that requires the computation of all previous terms to find the value of a_n.

• Explicit Formula

• Recursive Formula

• Arithmetic Formula

• Geometric Formula

Define a recursive function for the arithmetic sequence 4, 9, 14, 19, ...

A formula that requires the computation of all previous terms to find the value of t(n+1).

• Explicit Formula

• Recursive Formula

• Arithmetic Formula

• Geometric Formula