Question

write the explicit formula for each sequence. Then generate the first five terms a1= 5, r = 1 over 10

Answer 1

a geometric sequence?

Answer 2

yes

Answer 3

if it is geometric, then the terms look like
\[a,ar,ar^2,ar^3,ar^4,...\]

Answer 4

in your case \(a=5\) and \(r=\frac{1}{10}\) so the terms look like
\[5,5\times \frac{1}{10},5\times \left(\frac{1}{10}\right)^2,5\times \left(\frac{1}{10}\right)^3,...\]or
\[5,\frac{5}{10},\frac{5}{100},\frac{5}{1000},...\] or even
\[5,.5,.05,.005,...\]

Answer 5

Well this looks brand new to me my teacher didn't even explain the concept just gave us the work the week before exams.

Answer 6

"formula" is \(a_n=ar^{n-1}\) so in your case it will be
\[a_n=5\times \left(\frac{1}{10}\right)^{n-1}\] or
\[a_n=5\times \frac{1}{10^{n-1}}\] same thing

Answer 7

geometric: start with a number \(a\) like \(5\)
then multiply it by some other number \(r\) in your case \(r=\frac{1}{10}\)
then multiply it by the same \(r\) again, and again, and again
to get the terms of the sequence

Answer 8

Oh that makes sense thank you.