Question

Write a recursive sequence that represents the sequence defined by the
following explicit formula:
An = 1 - 5(n − 1)

Answer 1

Answer:

            $a_1=1\\a_n=a_{n-1}-5$

Step-by-step explanation:

a₁ = 1 - 5(1 - 1) = 1 - 5·0 = 1

a₂ = 1 - 5(2 - 1) = 1 - 5·1 = 1 - 5 = a₁ - 5

a₃ = 1 - 5(3 - 1) = 1 - 5·2 = 1 - 5 - 5 = a₂ - 5

a₄ = 1 - 5(4 - 1)  = 1 - 5·3 = 1 - 5 - 5 - 5 = a₃ - 5

and so on, therefore:

                              aₙ = aₙ₋₁ - 5