The first two terms of a geometric sequence are a1=1/3 and a2=1/6. What is a8, the eighth term?
r = a2/a1 remember?
then term 8 = a(r^7)
= .....
To find the eighth term of a geometric sequence, we need to determine the common ratio first.
The ratio between any two consecutive terms in a geometric sequence is constant. We can find the common ratio (r) by dividing any term by its preceding term.
In this case, we divide the second term, a2, by the first term, a1:
r = a2 / a1 = (1/6) / (1/3) = (1/6) * (3/1) = 1/2.
Now that we know the common ratio (r = 1/2), we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1),
where an represents the nth term, a1 is the first term, r is the common ratio, and n is the term number.
In this case, we want to find a8 (the eighth term), so we plug the values into the formula:
a8 = (1/3) * (1/2)^(8-1),
= (1/3) * (1/2)^7.
To simplify further:
a8 = (1/3) * (1/128),
= 1/384.
Therefore, the eighth term of the sequence is a8 = 1/384.