Write down the next three numbers and describe each pattern.

1) Write down the next three numbers and describe each pattern.

a) $3, 6, 9, 12, 15, 18, 21, \underline{24}, \underline{27}, \underline{30}$
The pattern is adding 3 to the previous term.
Next three numbers:
$21 + 3 = 24$
$24 + 3 = 27$
$27 + 3 = 30$
Description: Add 3 to the previous term.

b) $1, 8, 15, 22, 29, 36, 43, \underline{50}, \underline{57}, \underline{64}$
The pattern is adding 7 to the previous term.
Next three numbers:
$43 + 7 = 50$
$50 + 7 = 57$
$57 + 7 = 64$
Description: Add 7 to the previous term.

c) $7, 9, 8, 10, 9, \underline{11}, \underline{10}, \underline{12}$
The pattern alternates between adding 2 and subtracting 1.
Next three numbers:
$9 + 2 = 11$
$11 - 1 = 10$
$10 + 2 = 12$
Description: Alternate between adding 2 and subtracting 1.

d) $4, 1, 16, 1, 64, 1, \underline{256}, \underline{1}, \underline{1024}$
The pattern has two alternating sequences: the odd-positioned terms are powers of 4 ($4^1, 4^2, 4^3, \dots$), and the even-positioned terms are always 1.
Next three numbers:
The next odd-positioned term is $64 \times 4 = 256$.
The next even-positioned term is 1.
The next odd-positioned term is $256 \times 4 = 1024$.
Description: Odd terms are powers of 4 (multiplying by 4), and even terms are always 1.

e) $2, 4, 8, 16, 32, \underline{64}, \underline{128}, \underline{256}$
The pattern is multiplying the previous term by 2.
Next three numbers:
$32 \times 2 = 64$
$64 \times 2 = 128$
$128 \times 2 = 256$
Description: Multiply the previous term by 2.

2) Draw the next diagram.
I cannot answer this question as there are no diagrams provided in the image.