Question

find the rule of :
5,15,45,......,3645

Answer 1

I know that each number is multipled by 3, but i cannot figure out the rule.

Answer 2

r=45/15=3
\[tn =ar ^{n-1}=5*3^{n-1},where r=3,a=5\]

Answer 3

that's not it.. because if you put 100 in there it is only 300 and that is not correct..

Answer 4

when n=100
\[tn=5*3^{100-1}=5*\left( 3 \right)^{99}=5*3*3*3........99\times ,which is \neq 300 \]
but a very large no.

Answer 5

\[3645=5*3^{n-1},3^{n-1}=\frac{ 3645 }{5 }=729=3^{6}\]
n-1=6
n=6+1=7

Answer 6

\[t3=5*3^{3-1}=5*9=45\]
which is true.Because third term is 45.