Question

Shanna writes the formula f(x + 1) = 2.5f(x) when f(1) = 2 to represent this sequence: 2, 5, 12.5, 31.25, …
Which error did Shanna make?

Answer 1

let's think about what f(x + 1) = 2.5f(x) means

f(x) represents a generic term in the sequence for some x value

f(x+1) is the next value in the sequence

so f(x + 1) = 2.5f(x) means that, to generate any value in the sequence, multiply the previous value by 2.5

now, try to start with f(1) = 2, and keep multiplying by 2.5 to generate new terms. you'll notice a discrepancy between your terms and the germs she generated.