1) Write the first five temrs of the geometric sequence

1) a1 = 2

a2 = 2 sqrt3
a3 = 2sqrt3*sqrt3 = 6
a4 = 6*sqrt3
a5 = 6 sqrt3*sqrt2 = 18

2) an = 3*4/4^(n-1)
a1 = 3*4/4^0 = 12
a2 = 3
a3 = 3/4
a4 = 3/16
a5 = 3/64

Thank You

To find the first five terms of the geometric sequence where a1 = 2 and r = √3:

1) The formula to find the nth term of a geometric sequence is given by: an = a1 * r^(n-1)
2) In this case, a1 = 2 and r = √3. We need to find the first five terms, so we substitute the values of n from 1 to 5 into the formula to calculate each term.

Term 1 (n = 1): a1 * √3^(1 - 1) = 2 * 1 = 2
Term 2 (n = 2): a1 * √3^(2 - 1) = 2 * √3 = 2√3
Term 3 (n = 3): a1 * √3^(3 - 1) = 2 * (√3)^2 = 2 * 3 = 6
Term 4 (n = 4): a1 * √3^(4 - 1) = 2 * (√3)^3 = 2 * 3√3 = 6√3
Term 5 (n = 5): a1 * √3^(5 - 1) = 2 * (√3)^4 = 2 * 9 = 18

So, the first five terms of the geometric sequence are: 2, 2√3, 6, 6√3, 18.

Now, let's move on to the next question.

To find the nth term of the geometric sequence where a2 = 3, a5 = 3/64, and n = 1:

1) The formula to find the nth term of a geometric sequence is still: an = a1 * r^(n-1)
2) However, in this case, we are given a2 and a5, so we need to find a1 and r first.

Given a2 = 3,
Using the formula: a2 = a1 * r^(2-1), we can substitute a2 = 3 and n = 2 to find a1 and r.

3 = a1 * r

Given a5 = 3/64,
Using the formula: a5 = a1 * r^(5-1), we can substitute a5 = 3/64 and n = 5 to find a1 and r.

3/64 = a1 * r^4

Now, we have a system of equations:
Equation 1: 3 = a1 * r
Equation 2: 3/64 = a1 * r^4

By solving this system of equations simultaneously, we can find the values of a1 and r.

Once we find a1 and r, we can use the formula an = a1 * r^(n-1) with n = 1 to find the nth term.

Unfortunately, without the values of a1 and r, it is not possible to calculate the nth term of the geometric sequence.