Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

2.5, 6.25, 15.625, 39.0625, …
2.5, 5, 10, 20
–10, –7.5, –5, –2.5, …
–10, –25, 62.5, 156.25

Question

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

2.5, 6.25, 15.625, 39.0625, …
2.5, 5, 10, 20
–10, –7.5, –5, –2.5, …
–10, –25, 62.5, 156.25

Mercury · Answer

thoughts?

let's review what f (n + 1) = f(n) + 2.5 means
f(n) is a generic term in a sequence
f(n+1) is the next term

so f (n + 1) = f(n) + 2.5 means, that, to find a term in the sequence, take the previous term and add 2.5

can you try to see which sequence matches this rule?