Question

Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 4, -12, 36, ... Write your answer using decimals and integers. 30-1​

Answer 1

Explanation:

The sequence starts with 4 and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the equation to describe the sequence is:

aₙ = 4(-3)^(n-1)

where aₙ represents the nth term in the sequence.

Using this equation, we can find the values of the first few terms in the sequence as follows:

a₁ = 4(-3)^(1-1) = 4(1) = 4

a₂ = 4(-3)^(2-1) = 4(-3) = -12

a₃ = 4(-3)^(3-1) = 4(9) = 36

and so on.

Note that the index n starts at 1, but in some contexts it may start at 0, in which case we would need to adjust the exponent accordingly.