Since we know the first term (a₁) and the 3rd term (a₃), we can use the formula for a geometric sequence to find the common ratio:

a₃ = a₁ * r^(3-1)

We are given: a₁ = 5, a₃ = 45, and n = 3. Plugging in the values:

45 = 5 * r^(2)
9 = r^2

Now we solve for r:

r = 3

Now we have the first term and the common ratio, so we can find the 6th term using the formula:

aₙ = a₁ * r^(n - 1)

We are given: a₁ = 5, r = 3, and n = 6. Plugging in the values:

a₆ = 5 * 3^(6 - 1)
a₆ = 5 * 3^5
a₆ = 5 * 243

So, the 6th term of the geometric sequence is 1215. The correct answer is A) 1215.

To compute any term in a geometric sequence, we can use the formula:

aₙ = a₁ * r^(n - 1)

We are given: a₁ = 3, r = 2, and we need to find the 5th term, so n = 5. Plugging in the values:

a₅ = 3 * 2^(5 - 1)
a₅ = 3 * 2^4
a₅ = 3 * 16
a₅ = 48

So, the 5th term of the geometric sequence is 48. The correct answer is 48.

To find the common difference (d), we can subtract the first term from the second term, or the second term from the third term:

d = 5 - 3 = 2
d = 7 - 5 = 2

So, the common difference d is 2. The correct answer is 2.

To find the sum of the first 3 terms of a geometric sequence, we can use the formula:

S₃ = a₁ * (1 - r^3) / (1 - r)

We are given: a₁ = 1, r = 4. Plugging in the values:

S₃ = 1 * (1 - 4^3) / (1 - 4)
S₃ = 1 * (1 - 64) / (-3)
S₃ = (1 * -63) / (-3)
S₃ = 21

So, the sum of the first 3 terms of the geometric sequence is 21. The correct answer is 21.

To find the 3rd term of the geometric sequence, we can use the formula:

aₙ = a₁ * r^(n-1)

We are given: a₁ = 5, r = 0.5, and n = 3. Plugging in the values:

a₃ = 5 * 0.5^(3-1)
a₃ = 5 * 0.5^2
a₃ = 5 * 0.25
a₃ = 1.25

So, the 3rd term of the geometric sequence is 1.25. The correct answer is 1.25.