What is the ninth term of the following geometric sequence?
a4=27
a7=64
a9=
a+3d = 27
a+6d = 64
subtract them
3d = 37
d = 37/3
a + 3(37/3) = 27
a = -10
term(9) = a+8d
= -10 + 8(37/3) = 266/3
check:
term(4) = a+3d = -10 + 3(37/3) = 27
term(7) = a+6d = -10 + 6(37/3) = 64
To find the ninth term of a geometric sequence, we need to know either the common ratio or the fourth term (a4) and the seventh term (a7).
Given that a4 = 27 and a7 = 64, we can determine the common ratio (r) of the sequence.
The formula to calculate the common ratio (r) is:
r = (a7)^(1/(7-4))
In this case, (7-4) = 3, so we have:
r = (64)^(1/3)
To calculate the ninth term (a9), we can use the formula:
a9 = a7 * (r)^(9-7)
Substituting the known values, we have:
a9 = 64 * ((64)^(1/3))^(9-7)
Simplifying further, we have:
a9 = 64 * (64)^(2/3)
Now we can calculate the ninth term (a9).