The first term is 12.
The second term is 12r, where r is the common ratio. We multiply any term by the common ratio to get the next term.
The third term is (12r)*r = 12r^2.
The fourth term is (12r^2)*r = 12r^3
The fifth term is (12r^3)*r = 12r^4. The fifth term is also 20.27 which was given to us.
Equate the two items and solve for r.
12r^4 = 20.27
r^4 = 20.27/12
r = (20.27/12)^(1/4)
r = 1.14003484493186 which is approximate
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We can now find the approximate terms of this sequence
a = first term
a = 12
b = second term
b = a*r
b = 12*1.14003484493186
b = 13.6804181391823
c = third term
c = b*r
c = 13.6804181391823*1.14003484493186
c = 15.5961533719058
d = fourth term
d = c*r
d = 15.5961533719058*1.14003484493186
d = 17.7801582908741
e = fifth term
e = 17.7801582908741*1.14003484493186
e = 20.2700000000006
The 6 at the end is due to rounding error.
Therefore, the sequence has these five terms in the exact order shown
- 12
- 13.6804181391823
- 15.5961533719058
- 17.7801582908741
- 20.27
The sequence notation of this function is
{12, 13.6804181391823, 15.5961533719058, 17.7801582908741, 20.27}
Round those values however you need to.
