Answer:

1. 2, -6, 18, ... is -60.

2. 3, 12, 48, ... is 138.

3. 4, 20, 100, ... is 364.

Step-by-step explanation:

1. To find the sum of the first 5 terms of the sequence 2, -6, 18, ..., we can use the formula for the sum of an arithmetic sequence:

S_n = n/2(2a + (n-1)d)

where S_n is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

In this case, a = 2, d = -6 - 2 = -8, and n = 5. Substituting these values into the formula, we get:

S_5 = 5/2(2(2) + (5-1)(-8))

= 5/2(4 - 28)

= 5/2(-24)

= -60

Therefore, the sum of the first 5 terms of the sequence 2, -6, 18, ... is -60.

2. To find the sum of the first 6 terms of the sequence 3, 12, 48, ..., we can again use the formula for the sum of an arithmetic sequence:

S_n = n/2(2a + (n-1)d)

In this case, a = 3, d = 12 - 3 = 9, and n = 6. Substituting these values into the formula, we get:

S_6 = 6/2(2(3) + (6-1)(9))

= 6/2(6 + 40)

= 6/2(46)

= 138

Therefore, the sum of the first 6 terms of the sequence 3, 12, 48, ... is 138.

3. To find the sum of the first 7 terms of the sequence 4, 20, 100, ..., we can once again use the formula for the sum of an arithmetic sequence:

S_n = n/2(2a + (n-1)d)

In this case, a = 4, d = 20 - 4 = 16, and n = 7. Substituting these values into the formula, we get:

S_7 = 7/2(2(4) + (7-1)(16))

= 7/2(8 + 96)

= 7/2(104)

= 364

Therefore, the sum of the first 7 terms of the sequence 4, 20, 100, ... is 364.