Given the sequence 3,6,12,24,48,96
F. Write an explicit formula for the geometric sequence use your explicit formula to find the 32nd term of the sequence
To find the explicit formula for this geometric sequence, we need to identify the common ratio. We can do this by dividing any term in the sequence by its previous term.
Using the second term and the first term:
Common ratio = 6/3 = 2
Now that we have the common ratio, we can use the formula for a geometric sequence which is:
an = a1 * r^(n-1)
where an represents the nth term, a1 represents the first term, r represents the common ratio, and n represents the position of the term.
In this case, a1 = 3 and r = 2. So the explicit formula for this sequence is:
an = 3 * 2^(n-1)
To find the 32nd term, we substitute n = 32 into the formula:
a32 = 3 * 2^(32-1)
= 3 * 2^31
Calculating this, we find that the 32nd term of the sequence is:
a32 = 6,442,450,944.