How do you write the expression for the nth term of the geometric sequence $a_{1} = 1000, r = 1.005, n = 60$ $a_1=1000, r=1.005, n=60$ ?

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Answer 1 · 2017-04-24T12:55:03

$a_{n} = 1000 \times {1.005}^{n}$ $a_n=1000xx1.005^n$ and for $n = 60$ $n=60$ , $a_{60} = 1348.85$ $a_60=1348.85$

In a geometric sequence, where first term is $a_{1}$ $a_1$ and common ratio is $r$ $r$ ,

$n^{t h}$ $n^(th)$ term $a_{n}$ $a_n$ is given by $a_{1} \times r^{n - 1}$ $a_1xxr^(n-1)$

Hence $n^{t h}$ $n^(th)$ term of a geometric sequence whose first term is $a_{1} = 1000$ $a_1=1000$ and common ratio is $r = 1.005$ $r=1.005$ is

$a_{n} = 1000 \times {1.005}^{n}$ $a_n=1000xx1.005^n$

and $a_{60} = 1000 \times {1.005}^{60} ≅ 1000 \times 1.34885 = 1348.85$ $a_60=1000xx1.005^60~=1000xx1.34885=1348.85$ ,

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

How do you write the expression for the nth term of the geometric sequence a_1=1000, r=1.005, n=60a1=1000,r=1.005,n=60a_1=1000, r=1.005, n=60?