How do you identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80?

Question

9375 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-29T13:41:43

An explanation is given below.

We are to find $19$ th term of Geometric Sequence
Given $a_1 = 14$ and $a_9 = 358.80$

The general term of a Geometric Sequence is given by

$a_n = a*r^(n-1)$
Where $a$ is the first term also known as $a_1$ and $r$ is the common ratio.

We have $a_1$ if we get $r$ we can easily find $a_19$ by using $19$ for $n$

Let us start by writing the given term using $r$

$a_9 = a*r^8$

If we divide $a_9$ by $a_1$ we would get an equation in $r$

$(ar^8)/(a) = 358.80/14$

$r^8 = 25.628571428571428571428571428571$
Taking $8$ th root.

$r=root(8)(25.628571428571428571428571428571)$
#r=1.4999975504465127405341330547934"

$r~~ 1.5$

$a_19 = 14(1.5)^19$

$a_19 = 31,035.729480743408203125"$
$a_19 ~~ 31035.73$