Question

Hat is the recursive formula for the sequence defined by the explicit equation an=15-3n

Answer 1

• a₁ = 12
• aₙ = aₙ₋₁ - 3

Explanation:

Recursive formula is used to represent the terms using the previous term of the sequence.

Using the explicit equation find the first two terms and their difference:

• a₁ = 15 - 3*1 = 15 - 3 = 12
• a₂ = 15 - 3*2 = 15 - 6 = 9

• d = a₂ - a₁ = 9 - 12 = - 3

The recursive formula for this sequence is:

• a₁ = 12
• aₙ = aₙ₋₁ - 3