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

1 Answer
Dec 29, 2015

Answer:

An explanation is given below.

Explanation:

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#