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 6th term of the arithmetic sequence, we can use the formula:

aₙ = a₁ + (n-1)d

We are given: a₁ = 2, d = 2, and n = 6. Plugging in the values:

a₆ = 2 + (6-1)(2)
a₆ = 2 + 10
a₆ = 12

So, the 6th term of the arithmetic sequence is 12. The correct answer is  12.

First, we need to determine the common difference (d) between consecutive terms in the arithmetic sequence. Using the formula:

aₙ = a₁ + (n - 1)d

We are given: a₁ = 2, a₅ = 50, and n = 5. Plugging in the values:

50 = 2 + (5 - 1)d
48 = 4d

Now we solve for d:

d = 12

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

Sₙ = n * (a₁ + aₙ) / 2

Since we have d = 12 and want to find the sum for the first 10 terms, we need to find a₁₀:

a₁₀ = a₁ + (n - 1)d
a₁₀ = 2 + (10 - 1) * 12
a₁₀ = 2 + 108
a₁₀ = 110

Now we can calculate the sum:

S₁₀ = 10 * (2 + 110) / 2
S₁₀ = 10 * 112 / 2
S₁₀ = 5 * 112

So, the sum of the first 10 terms of this arithmetic sequence is 560. The correct answer is 560.

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.

To find the 5th term of the arithmetic sequence, we can use the formula:

aₙ = a₁ + (n-1)d

We are given: a₁ = 4, d = -1, and n = 5. Plugging in the values:

a₅ = 4 + (5-1)(-1)
a₅ = 4 - 4
a₅ = 0

So, the 5th term of the arithmetic sequence is 0. The correct answer is) 0.