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.
89, -178, 356, …
The given sequence is an alternating sequence where each term is obtained by multiplying the previous term by -2.
To write an equation to describe the sequence, we can use the formula:
aₙ = a₁ * r^(n-1)
Where:
aₙ represents the nth term in the sequence
a₁ is the first term in the sequence
r is the common ratio between consecutive terms
n is the position of a term in the sequence (starting at 1 for the first term)
Since the common ratio between consecutive terms is -2, the equation becomes:
aₙ = 89 * (-2)^(n-1)