The pattern is as follows: add 2, multiply by 2, subtract 2;  add 3, multiply by 3, subtract 3; keep working this same sequence of operations with consecutive whole numbers. Examine below:

\(\displaystyle 1+ 2 = 3\)

\(\displaystyle 3 \times 2 = 6\)

\(\displaystyle 6 - 2 = 4\)

\(\displaystyle 4+ 3 = 7\)

\(\displaystyle 7 \times 3 = 21\)

\(\displaystyle 21 - 3 = 18\)

\(\displaystyle 18 + 4 = 22\)

Multiply by 4 to fill in the blank:

\(\displaystyle 22 \times 4 = \underline{88}\)

Continuing the pattern, we see this is correct:

\(\displaystyle 88 - 4 = 84\)

\(\displaystyle 84 + 5 = 89\)

\(\displaystyle 89 \times 5 = 445\)

Subtract 1, then 2, then 3, and so forth; the amount subtracted increases by 1 each time, as shown:

\(\displaystyle 1000 - 1 = 999\)

\(\displaystyle 999 - 2= 997\)

\(\displaystyle 997 - 3 = 994\)

\(\displaystyle 994 - 4 = 990\)

\(\displaystyle 990 - 5 = 985\)

Subtract 6 to get the missing term:

\(\displaystyle 985 - 6 = \underline{979}\)

Continuing the pattern, we confirm this is correct:

\(\displaystyle 979 - 7 = 972\)

\(\displaystyle 972 - 8 = 964\)

Alternately add 4 and 8 to each term, as follows:

\(\displaystyle 12+ 4 = 16\)

\(\displaystyle 16+ 8 = 24\)

\(\displaystyle 24+ 4 = 28\)

\(\displaystyle 28+ 8 = 36\)

Add 4 to get the missing term:

\(\displaystyle 36+ 4 = \underline{40 }\)

Continuing the pattern, we see this is correct:

\(\displaystyle 40 + 8 = 48\)

\(\displaystyle 48+ 4 = 52\)

The terms of the sequence are obtained by alternately multiplying by \(\displaystyle -2\) and subtracting 5, as seen below:

\(\displaystyle -10 \times (-2) = 20\)

\(\displaystyle 20 - 5 = 15\)

\(\displaystyle 15 \times (-2) = -30\)

\(\displaystyle -30 - 5 = -35\)

\(\displaystyle -35 \times (-2) = 70\)

\(\displaystyle 70- 5 = 65\)

Multiply by \(\displaystyle -2\) to obtain the next term:

\(\displaystyle 65 \times (-2) =\underline{ -130}\)

Continuing the pattern, we see that this is correct:

\(\displaystyle -130- 5 = -135\)

\(\displaystyle -135 \times (-2) = 270\)

There are two alternating patterns in this series. The first is add \(\displaystyle 2\) each time:

\(\displaystyle 2,4,6,8\)

The second is to multiply by \(\displaystyle 2\) each time:

\(\displaystyle 10,20,40\)

The blank belongs to the second pattern. The last operation is \(\displaystyle 40\cdot2=80\)

The pattern is to add \(\displaystyle 32\) each time. The last operation is \(\displaystyle 101+32=133\).

The pattern is to multiply by \(\displaystyle -2\) each time. The last operation is \(\displaystyle 2.48\cdot-2=-4.96\)

The are two alternating patterns in this series. The first is to add \(\displaystyle 20\) each time:

\(\displaystyle 13,33,53\)

The second is to add \(\displaystyle 1\) each time:

\(\displaystyle .5,1.5,2.5,\)

The blank belongs in the first pattern. The last operation is \(\displaystyle 53+20=73\).

The pattern is to multiply by \(\displaystyle 3\) each time. The last operation is \(\displaystyle 13.5\cdot3=40.5\).

The pattern is to multiply by \(\displaystyle 2\), then add \(\displaystyle 3\). The operation before the blank is \(\displaystyle 29\cdot2=58\).