What is the 7th term of the geometric sequence where a1 = -625 and a2 = 125?

Jul 17, 2015

Answer:

The seventh term of the sequence is $\textcolor{red}{- \frac{1}{25}}$.

Explanation:

We first find the common ratio $r$ by dividing a term by its preceding term.

$r = {a}_{2} / {a}_{1} = \frac{125}{- 625}$

$r = - \frac{1}{5}$

Now we use the ${n}^{\text{th}}$ term rule:

${t}_{n} = a {r}^{n - 1}$, where $a$ is the first term and $r$ is the common ratio

t_7 = -625(-1/5)^(7-1) = -625(-1/5)^6 = -(5^4)(-1)^6/5^6 = -(5^4 × 1)/5^6 = -5^4/5^6 = -1/5^2

${t}_{7} = - \frac{1}{25}$