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 sum of terms in a finite arithmetic sequence, we can use the formula:

Sₙ = n * (a₁ + aₙ) / 2

We are given: a₁ = 1, aₙ = 19, and n = 10. Plugging in the values:

S₁₀ = 10 * (1 + 19) / 2
S₁₀ = 10 * 20 / 2
S₁₀ = 100

So, the sum of the terms in this arithmetic sequence is 100. The correct answer is 100.

Since we know the first term (a₁) and the 4th term (a₄), we can use the formula for a geometric sequence to find the common ratio:

aₙ = a₁ * r^(n - 1)

We are given: a₁ = 1, a₄ = -27, and n = 4. Plugging in the values:

-27 = 1 * r^(4 - 1)
-27 = r^3

Now we solve for r:

r = -3

So, the common ratio r is -3. The correct answer is -3.

To find the 4th term of the geometric sequence, we can use the formula:
aₙ = a₁ * r^(n-1)

We are given: a₁ = 3, r = 2, and n = 4. Plugging in the values:

a₄ = 3 * 2^(4-1)
a₄ = 3 * 2^3
a₄ = 3 * 8
a₄ = 24

So, the 4th term of the geometric sequence is 24. The correct answer is 24.

To find the sum of the first 6 terms of a geometric sequence, we can use the formula:

Sₙ = a₁ * (1 - r^n) / (1 - r)

We are given: a₁ = 4, r = 3, and n = 6. Plugging in the values:

S₆ = 4 * (1 - 3^6) / (1 - 3)
S₆ = 4 * (1 - 729) / (-2)
S₆ = 4 * 728 / 2
S₆ = 4 * 364

So, the sum of the first 6 terms of this geometric sequence is 1456. The correct answer is) 1456.