Find the indicated nth term of the geometric sequence.
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
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 = .....
Thank you!
It actually makes sense now.
To find the indicated nth term of a geometric sequence, you need two pieces of information: the value of the term you know (in this case, either a5 or a9), and the position of the term you want to find (in this case, the 7th term).
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.