What is the explicit rule for this geometric sequence? 10, 100, 1000, 10,000

Answer 1

a_n = 10ⁿ

The nth term is 10 raised to the nth power, so the first term is 10¹ = 10, the second is 10² = 100 and so on.

Answer 2

Since you need both a ratio and a first term for writing an explicit rule a_n=a₁(r)^n-1, first find the ratio between consecutive terms. This means, divide the 2nd term by the 1st -- 100/10 -- and you get the ratio 10. Double check it with the 3rd term divided by the 2nd -- 1000/100 -- and you also get 10. The first term in the entire sequence is 10. So the explicit rule for this geometric sequence is a_n=10 (10)^n-1. Hope that helps!