1) Write the first five temrs of the geometric sequence

a1 = 2 r=sqrt3

I know the first term is 2 but the sqrt 3 threw me off so I do not know how to find the next numbers.

2) Find the nth term of the geometric sequence.

a2 = 3 a5 = 3/64 n=1

I know the formula is a1^r n-1 but I do not know how to find a1.

Answered Already

2

2 sqrt 3
2*3 = 6
6 sqrt 3
6*3 = 18
18 sqrt 3
18*3 = 54 etc

a1

a1 r = 3
a1 r^2
a1 r^3
a1 r^4 = 3/64

so
a1 = 3/r

( 3 r^4/r) = 3/64
r^3 = 1/64 = 1/2^6
r = 1/2^2
r = 1/4
a1 = 12

1) To find the first five terms of the geometric sequence with the given values, you 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.

Given that a1 = 2 and r = √3, we can substitute these values into the formula to find the first five terms:

a1 = 2
a2 = a1 * r^(2-1) = 2 * (√3)^1 = 2 * √3 = 2√3
a3 = a1 * r^(3-1) = 2 * (√3)^2 = 2 * 3 = 6
a4 = a1 * r^(4-1) = 2 * (√3)^3 = 2 * 3√3 = 6√3
a5 = a1 * r^(5-1) = 2 * (√3)^4 = 2 * 9 = 18

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

2) To find the nth term of a geometric sequence, you can use the formula you mentioned:

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, you want to find the nth term given a2 = 3, a5 = 3/64, and n = 1.

By substituting the given values into the formula, we can solve for a1:

3 = a1 * r^(2-1)
3/64 = a1 * r^(5-1)

Since n = 1, we have:

3 = a1 * r^0

Since any number to the power of 0 is 1, the equation simplifies to:

3 = a1

Therefore, a1 is equal to 3.

Using the formula for the nth term, we can now find any term in the geometric sequence:

an = a1 * r^(n-1)

For example, to find the 2nd term (a2), we substitute a1 = 3, r = a2/a1, and n = 2:

a2 = a1 * r^(2-1) = 3 * (a2/3)^(2-1)

To find the value of a2, we need more information about the relationship between a2 and a1. Please provide additional information or clarify the question.