Question

Which one is a rule for the nth term of the sequence 3, 15, 75, 375...?

Answer 1

By dividing consecutive terms:
15 / 3 = 5
75 /15 = 5
we find that this is a geometric series with a common ratio of 5 (k = 5).

We can then plug this into the general formula for a geometric series:
\[x _{n}=a _{o}\times k ^{n-1}\]
where x is the term you're solving for and a is the first term.

With this, we get:
\[x _{n}=3 \times 5^{n-1}\]