How do you find the nth term rule for 2,10,50,250,...?

Aug 3, 2016

${n}^{t h}$ term = ${t}_{n} = 2 \cdot {5}^{n - 1}$, where, $n \in \mathbb{N}$.

Explanation:

Let us note that, in the given seq., every succeeding term is obtained by multiplying by $5$ the preceding term.

In other words, this means that the given seq. is a Geometric Seq. with Common Ratio $r = 5$.

The seq. has the First Term $a = 2$.

The Formula for the General Term, or, ${n}^{t h}$ term, denoted as ${t}_{n}$ is given by, ${t}_{n} = a \cdot {r}^{n - 1}$.

In our case, ${t}_{n} = 2 \cdot {5}^{n - 1}$, where, $n \in \mathbb{N}$.