I thought I understood this and there was a question earlier and I guessed at the right answer, but I need to know exactly how to do this. Take the geometric sequence: 9, 18, 36, 72,... Write a rule for the nth term and then use the rule to find the 20th term.
Thanks a bunch if you could show the steps.
Thanks a bunch if you could show the steps.
-
First find the common ratio:
18/9 = 2
36/18 = 2
72/36 = 2
Therefore the common ratio or r=2
And so the general formula is
a_n = (a_1)r^(n-1)
And for this sequence the rule would be
a_n = (9)2^(n-1)
And then to compute the 20th term
a_20 = (9)2^(20-1)
= (9)2^19
= 4718592
:)
18/9 = 2
36/18 = 2
72/36 = 2
Therefore the common ratio or r=2
And so the general formula is
a_n = (a_1)r^(n-1)
And for this sequence the rule would be
a_n = (9)2^(n-1)
And then to compute the 20th term
a_20 = (9)2^(20-1)
= (9)2^19
= 4718592
:)
-
Okay, So you need to order all the terms, Which you've done. Next, you divide them into each other to find the common ratio. This would be 18/9 = 2. 36/18 = 2. 72/36 = 2. This is r.
The basic look for a geometric series equation is
an=a1*[(r)^n-1] With r being the common ratio and a1 being your first term.
So for the 20th term, You would just plug everything in
a20=9*[(2)^20-1]
a20=9*524288
a20=4718592
The basic look for a geometric series equation is
an=a1*[(r)^n-1] With r being the common ratio and a1 being your first term.
So for the 20th term, You would just plug everything in
a20=9*[(2)^20-1]
a20=9*524288
a20=4718592