What is the recursive rule for the sequence? -2.7, -8.3, -13.9, -19.5, -25.1,…

Solution:

A recursive formula consists of the first term and the difference between successive terms, a_n+1 = a_n + d.

⇒ d = a_n+1 - a_n

Given sequence is -2.7, -8.3, -13.9, -19.5, -25.1,…

Put n = 1; d = a₂ - a₁ = -8.3 - (-2.7) = -5.6

Put n = 2; d = a₃ - a₂ = -13.9 - (-8.3) = -5.6

Hence, the difference between the successive terms is the same.

a_n+1 = a_n -5.6

Therefore, the recursive rule for every successive term is written by adding -5.6.

What is the recursive rule for the sequence? -2.7, -8.3, -13.9, -19.5, -25.1,…

Summary:

The recursive rule for the sequence -2.7, -8.3, -13.9, -19.5, -25.1,… is adding -5.6.