Which term in the sequence 5, 15, 45,.... has a value of 3645?

Question

I have U1 = 5, r= 15/3 and Un=3645.


U1 x r^n-1 =3645
5(3)^n-1 = 3645,
I divide both sides by 5
(3)^n-1 = 729,
but not sure what to do next  or maybe there is another to solve this (easier)! Thank you in advance for your help.

Answer 1

you are doing very well so far

3^(n-1)=729

factor 729 to get 3*3*3*3*3*3=3^6

3^(n-1)=3^6

since the bases are equal the exponents must be equal also

n-1=6

n=6+1

n=7

3645 is the 7th term

5, 15, 45, 135, 405, 1215, 3645

you could also have used logarithms

log3^(n-1)=log729

(n-1)log3=log729

n-1=log729/log3

n-1=2.8627/0.4771

n-1=6.00021 which is approximate but you can see it is 6 and the more digits you use the more accurate 6 becomes