# How do you find the 5th term of the sequence in which t_1 = 8 and t_n = -3t_n-1?

Dec 16, 2015

${t}_{5} = 648$

#### Explanation:

Given the sequence ${t}_{1} = 8 , {t}_{n} = - 3 {t}_{n - 1}$ we have

${t}_{1} = 8$

${t}_{2} = - 3 {t}_{1} = - 24$

${t}_{3} = - 3 {t}_{2} = 72$

${t}_{4} = - 3 {t}_{3} = - 216$

${t}_{5} = - 3 {t}_{4} = 648$

Note that in general, as every term after the first is just $- 3$ multiplied by the previous term, we can express the ${n}^{t h}$ term directly as

${t}_{n} = {\left(- 3\right)}^{n - 1} {t}_{1} = {\left(- 3\right)}^{n - 1} \cdot 8$

In general, a sequence of the form

$a , a r , a {r}^{2} , a {r}^{3} , \ldots , a {r}^{n} , \ldots$

is called a geometric sequence.