# How do you write the expression for the nth term of the geometric sequence a_1=1000, r=1.005, n=60?

##### 1 Answer
Apr 24, 2017

${a}_{n} = 1000 \times {1.005}^{n}$ and for $n = 60$, ${a}_{60} = 1348.85$

#### Explanation:

In a geometric sequence, where first term is ${a}_{1}$ and common ratio is $r$,

${n}^{t h}$ term ${a}_{n}$ is given by ${a}_{1} \times {r}^{n - 1}$

Hence ${n}^{t h}$ term of a geometric sequence whose first term is ${a}_{1} = 1000$ and common ratio is $r = 1.005$ is

${a}_{n} = 1000 \times {1.005}^{n}$

and ${a}_{60} = 1000 \times {1.005}^{60} \cong 1000 \times 1.34885 = 1348.85$,

where value of ${1.005}^{60}$ has been approximated up to $5 \mathrm{dp}$.