Write the missing numbers in each number pattern. (a) 321, 323, 325, ____, 329, 331, ____ (b) 278, 275, 272, ____, 266, 263, ____ (c) 205, 207, 204, 206, 203, 205, 202, ____, 203, 200 (d) 101, 106, 102, 107, 103, 108, 104, ____, 110, ____, 111, 107

Let's look at each number pattern individually to identify and fill in the missing numbers.
(a) The pattern is: 321, 323, 325, ____, 329, 331, ____.
Here, we notice that each consecutive number increases by 2. So, starting from 321:

321 + 2 = 323
323 + 2 = 325
325 + 2 = 327 (missing number)
327 + 2 = 329
329 + 2 = 331
331 + 2 = 333 (missing number)

Therefore, the missing numbers are 327 and 333.
(b) The pattern is: 278, 275, 272, ____, 266, 263, ____.
Here, we see that each consecutive number decreases by 3. So, starting from 278:

278 - 3 = 275
275 - 3 = 272
272 - 3 = 269 (missing number)
269 - 3 = 266
266 - 3 = 263
263 - 3 = 260 (missing number)

Therefore, the missing numbers are 269 and 260.
(c) The pattern is: 205, 207, 204, 206, 203, 205, 202, ____, 203, 200.
This pattern alternates between adding 2 and subtracting 3. Let's follow this pattern:

205 + 2 = 207
207 - 3 = 204
204 + 2 = 206
206 - 3 = 203
203 + 2 = 205
205 - 3 = 202
202 + 2 = 204 (missing number)
204 - 3 = 203
203 + 2 = 205
205 - 3 = 202
202 + 2 = 204
204 - 3 = 201

Hence, the missing number is 204.
(d) The pattern is: 101, 106, 102, 107, 103, 108, 104, ____, 110, ____, 111, 107.
This sequence alternates between adding 5 and adding 1. Let's use this pattern:

101 + 5 = 106
106 + 1 = 107
107 + 5 = 112
112 + 1 = 113
113 + 5 = 118
118 + 1 = 119
119 + 5 = 124
124 + 1 = 125
125 + 5 = 130
130 + 1 = 131

Following this method, the missing roles are 109 and 111 in this order.
Together, the complete sequences with missing numbers filled in are:
(a) 321, 323, 325, 327, 329, 331, 333 (b) 278, 275, 272, 269, 266, 263, 260 (c) 205, 207, 204, 206, 203, 205, 202, 204, 203, 200 (d) 101, 106, 102, 107, 103, 108, 104, 109, 110, 111, 111, 107

Answered by danjohnbrain | 2025-07-22

The missing numbers for the sequences are: (a) 327 and 333, (b) 269 and 260, (c) 201, and (d) 112 and 113. Each pattern consists of consistent additions and subtractions. The identified patterns help us fill in the missing values correctly.
;

Answered by danjohnbrain | 2025-08-10