Question

find the missing term of each geometric sequence
-20, __, __, __, -1.25

Answer 1

help i think i know how to do this but not sure @whpalmer4

Answer 2

since it's a geometric sequence you're looking for a factor, so it's
-20(x)^4 = -1.25

Answer 3

if you replace x by 0.5 you get
-20, -10, -5, -2.5, -1.25

Answer 4

im still lost how did you get that 0.o

Answer 5

\[a_5 = a*r^{5-1}\]\[a_1 = a*r^{1-1} = a*r^0 = a*1\]

Answer 6

ok so what do we do after

Answer 7

Okay, so \[a_1 = a\]or\[a = a_1 = -20\]
\[a_n = -20r^{n-1}\]\[a_5 = -1.25 = -20r^{5-1}\]

Answer 8

ok so..... still alittle confused

Answer 9

This is just like the problems we did finding the equation for an arithmetic sequence, except we are multiplying instead of adding...

We know 2 terms: \(a_1 = -20\) and \(a_5 = -1.25\)
Good so far?

Answer 10

We know the general formula for the \(n\)th term is \[a_n = a*r^{n-1}\]

Answer 11

yes ok i get it

Answer 12

Let's plug in \(n=1\), because we know \(a_1 = -20\)
\[a_1 = a*r^{1-1}\]\[-20 = a*r^0\]\[-20 = a*1\]\[a=-20\]
So now our formula has evolved to
\[a_n = -20r^{n-1}\]

Answer 13

Let's plug in \(a_5\):
\[a_5 = -20 r^{5-1}\]\[-1.25 = -20r^4\]\[\frac{-1.25}{-20} = r^4\]

Answer 14

it will =0.5 right

Answer 15

at this point it might be less confusing if we convert the fraction on the left to a regular fraction with no decimals. 1.25 = 5/4, right? We can drop the two negative signs because they cancel each other out, so that gives us
\[\frac{\frac{5}{4}}{20}=\frac{1}{16} = r^4\]\[2^4=16\]so \[r=\frac{1}{2}\]and our formula is \[a_n = -20(\frac{1}{2})^{n-1}\]or if you prefer
\[a_n = -20(2)^{1-n}\]

Answer 16

ok i get it thank you i have one more like this i will post it as a new question is that ok

Answer 17

of course