what is the nth term equation for a geometric sequence with a1 = 36 and r = 1/3
term(9) = a(r^8) = 36(1/3)^8 = 36/6561 = 4/729
The nth term equation (an) for a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.
To find the nth term equation for the given geometric sequence with a1 = 36 and r = 1/3, we substitute these values into the formula.
Thus, the nth term equation for this geometric sequence is: an = 36 * (1/3)^(n-1).
To find the nth term equation for a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
Where:
- an is the nth term of the sequence
- a1 is the first term of the sequence
- r is the common ratio of the sequence
- n is the position of the term in the sequence
In your case, you're given a1 = 36 and r = 1/3. So let's substitute these values into the formula:
an = 36 * (1/3)^(n-1)
This equation gives you the general formula for finding the nth term in the geometric sequence. To find a specific term, substitute the term number (n) into the equation. For example, if you want to find the 5th term of the sequence, substitute n = 5 into the equation:
a5 = 36 * (1/3)^(5-1)
= 36 * (1/3)^4
= 36 * (1/81)
= 36/81
= 4/9
Therefore, the 5th term of the sequence is 4/9.
I really have to get new glasses, I read it as the 9th term
term(n) = 36(1/3^(n-1)
or 36(3)^(1-n)
= 4(3^2)(3^(1-n)
= 4(3)^(3-n)