Recursive and Explicit Arithmetic Sequence

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)

What is the common difference of the sequence 2, -1, -4, -7,...?

• -3

• -1

• -2

• 3

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

(HINT - Find the explicit formula first, then use your formula!)

• -216

• -148

• -146

• -150

Find 26th term in the arithmetic sequence: -15, -35, -55, -75, ...

(HINT - Find the explicit formula first, then use your formula!)

• -515

• -490

• -535

• 460

Select the explicit rule that represents the sequence.

• a(n) = 6 + 5(n - 1)

• a(n) = 4 + 6(n - 1)

• a(n) = 6 - 4(n - 1)

Select the explicit rule that represents the sequence.

• a(n) = 14(-3)(n - 1)

• a(n) = 3 + (n - 1)(14)

• a(n) = 14 + (n - 1)(-3)

• a(n) = -3 + (n - 1)(14)

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

• -16, -21, -26, -31

• 5, -11, -27, -43

• -16, -80, -500, -200

• -16, -11, -6, -1

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1 - 1

• 14

• 13

• 17

• 16

Write a recursive rule for the sequence a_n = 17 + (n-1)(-16)

• a₁ = 17
  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

Find the common difference: -34, -29, -24, -19, ...

• d = -5

• d = 5

• d = -6

• d = 6