find the 7and11 term of the gp 81 27 9
To find the 7th and 11th terms of the geometric progression (GP) with the terms 81, 27, and 9, we need to first find the common ratio (r) of the GP.
The common ratio (r) can be found by dividing any term by its preceding term. Let's take the second term (27) divided by the first term (81):
r = 27 / 81
r = 1/3
Now, we can use the formula to find the nth term of a GP:
nth term = a * r^(n-1)
For the 7th term (n = 7), we have:
7th term = 81 * (1/3)^(7-1)
7th term = 81 * (1/3)^6
7th term = 81 * (1/729)
7th term = 81/729
7th term = 1/9
So, the 7th term of the GP is 1/9.
For the 11th term (n = 11), we have:
11th term = 81 * (1/3)^(11-1)
11th term = 81 * (1/3)^10
11th term = 81 * (1/59049)
11th term = 81/59049
So, the 11th term of the GP is 81/59049.
81 27 9
sure looks like a = 81 and r = 1/3
term(7) = ar^6 = 81(1/3)^6
= 81/729
= 1/9
I will let you do term(11)