If 32/9and81/2 are the first and last termo respectively of a geometric sequence determine the values of the fifth term id the are steven terms in the sequence
To find the values of the fifth term in a geometric sequence where the first term is 32/9 and the last term is 81/2, we need to find the common ratio first.
The common ratio (r) of a geometric sequence can be found by dividing any term by the previous term. So, in this case, we can find the common ratio by:
r = (Second Term) / (First Term) = (81/2) / (32/9) = (81/2) * (9/32) = 729/64
Now that we have the common ratio, we can find the fifth term. The formula for finding the nth term in a geometric sequence is:
Tn = a * r^(n-1)
where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number.
So, to find the fifth term (n=5):
T5 = (32/9) * (729/64)^(5-1)
T5 = (32/9) * (729/64)^4
T5 = (32/9) * (531441/256)
T5 = 5855264/576
Therefore, the fifth term in the geometric sequence is 5855264/576 or approximately 10173.72.