Question

134, 108, 82, 56, ...
Recursive Rule
Explicit Rule

Answer 1

• a) a₁ = 134, aₙ = aₙ₋₁ - 26
• b) aₙ = 160 - 26n

Explanation:

Given sequence:

• 134, 108, 82, 56, ...

This is an AP since the difference of terms is common:

• d = 56 - 82 = 82 - 108 = 108 - 134 = - 26

The first term is:

• a₁ = 134

Recursive formula for this sequence is:

• a₁ = 134, aₙ = aₙ₋₁ - 26

The explicit formula is:

• aₙ = a₁ + (n - 1)d

Substitute the values to get:

• aₙ = 134 + (n - 1)(- 26) = 134 - 26n + 26 = 160 - 26n