term5 = ar^4 = -2/81
term9 = ar^8 = -2/6561
divide term9 equation by term 5 equation, that is ...
ar^8/ar^4 = (-2/6561) / (-2/81)
r^4 = 1/81
r = ± 1/3
sub that back into ar^4 = -2/81
a(1/81) = -2/81
a = -2
now term7 = ar^6 = .....
7th term
a5: -2/81
a9: -2/6561
I know the formula is
an= a1 r ^ n-1
but I can't figure out how to apply it
term9 = ar^8 = -2/6561
divide term9 equation by term 5 equation, that is ...
ar^8/ar^4 = (-2/6561) / (-2/81)
r^4 = 1/81
r = ± 1/3
sub that back into ar^4 = -2/81
a(1/81) = -2/81
a = -2
now term7 = ar^6 = .....
It actually makes sense now.
Let's first calculate the common ratio (r) using the formula:
r = (a9 / a5)
Substituting the given values:
r = (-2/6561) / (-2/81)
r = (-2/6561) * (-81/2)
r = 6561
Now that we know the common ratio (r = 6561), we can calculate the first term (a1) using either a5 or a9. Let's use a5. Rearranging the formula, we have:
a1 = (a5 / r^(5-1))
Substituting the given values:
a1 = (-2/81) / (6561^(5-1))
a1 = (-2/81) / (6561^4)
a1 = (-2/81) / 18,014,398,509,481
Now that we have the first term (a1), we can calculate the 7th term (a7) using the formula:
a7 = (a1 * r^(7-1))
Substituting the known values:
a7 = (-2/81) / 18,014,398,509,481 * 6561^(7-1)
a7 = (-2/81) / 18,014,398,509,481 * 6561^6
Now, you can simplify the expression and perform the calculations to find the value of the 7th term in the geometric sequence.