Find a12 for the following geometric sequence.
1/32, 1/16, 1/8,
r = (1/16)/(1/32) = 2
term(12) = a r^11
= (1/32) (2)^11
= (1/32)(2048 = 64
To find the 12th term (a12) of the geometric sequence given, we first need to determine the common ratio (r).
The common ratio (r) is found by dividing any term by its previous term. In this case, we can divide each term by its previous term to find the common ratio:
r = (1/16) / (1/32) = (1/16) * (32/1) = 2
Now that we know the common ratio (r = 2), we can use the formula to find the nth term of a geometric sequence:
an = a1 * r^(n-1)
In this formula, a1 represents the first term, r represents the common ratio, and n represents the position of the term we want to find (in this case, a12).
Plugging in the values, we have:
a12 = (1/32) * 2^(12-1) = (1/32) * 2^11 = (1/32) * 2048 = 64
Therefore, the 12th term (a12) of the geometric sequence is 64.