Question

Write a recursive formula for the sequence –2, 4, –8, 16, ... please help and thank you

Answer 1

-2,4,-8,16,...

a₁ = -2

a₂ = -2a₁

a₃ = -2a₂

..................

=> aₙ₊₁ = -2•aₙ, with a₁ = -2

Answer 2

Answer:

see explanation

Step-by-step explanation:

A recursive formula allows us to calculate any term in the sequence from the previous term.

These are the terms of a geometric sequence with r being the common ratio between consecutive terms.

r = 4 ÷ - 2 = - 8 ÷ 4 = 16 ÷ - 8 = - 2

Multiplying a particular term by - 2 gives the next term in the sequence.

Hence recursive formula is

$a_{n+1}$ = - 2 $a_{n}$ with a₁ = - 2