102,105,111,114,120,123,129,_,_,_,_,_, 201,204,210,213,219
The pattern is:
+3 + 6 + 3 + 6 . . .
+3+6 is wrong
To find the missing numbers in the sequence: 102, 105, 111, 114, 120, 123, 129, __, __, __, __, __, 201, 204, 210, 213, 219, we need to identify the pattern.
Looking at the numbers, we can observe that the sequence starts with an incremental pattern and then switches to a different pattern. Let's analyze it further:
The first pattern:
102, 105, 111, 114, 120, 123, 129
In this pattern, each number is increasing by 3:
102 + 3 = 105
105 + 6 = 111
111 + 3 = 114
114 + 6 = 120
120 + 3 = 123
123 + 6 = 129
The second pattern:
__ , __ , __ , __ , __ , 201, 204, 210, 213, 219
In this pattern, the numbers seem to be increasing by 3 at first and then by 9:
__ + 3 = __
__ + 3 = __
__ + 3 = __
__ + 3 = __
__ + 3 = __
__ + 27 = 201
201 + 3 = 204
204 + 6 = 210
210 + 3 = 213
213 + 6 = 219
Using this information, we can fill in the missing numbers in the sequence:
__ , __ , __ , __ , __ , 201, 204, 210, 213, 219
__ = 129 + 3 = 132
__ = 132 + 6 = 138
__ = 138 + 3 = 141
__ = 141 + 6 = 147
__ = 147 + 3 = 150
Therefore, the missing numbers in the sequence are: 132, 138, 141, 147, 150
To find the missing numbers in the given sequence, let's analyze the pattern:
Starting from the first few numbers: 102, 105, 111, 114, 120, 123, 129, ...
Now let's look at the difference between consecutive numbers:
105 - 102 = 3
111 - 105 = 6
114 - 111 = 3
120 - 114 = 6
123 - 120 = 3
129 - 123 = 6
By observing the differences, we can see that the pattern alternates between adding 3 and adding 6.
So, if we continue this pattern, we can find the missing numbers:
To get the next number after 129, we add 6: 129 + 6 = 135
Then, we add 3: 135 + 3 = 138
Again, add 6: 138 + 6 = 144
Add 3: 144 + 3 = 147
Finally, add 6: 147 + 6 = 153
Therefore, the missing numbers in the sequence are: 135, 138, 144, 147, 153.
Now let's analyze the second part of the given sequence:
201, 204, 210, 213, 219, ...
Similar to the first part, let's find the differences between consecutive numbers:
204 - 201 = 3
210 - 204 = 6
213 - 210 = 3
219 - 213 = 6
We can observe that the pattern here is also alternating between adding 3 and adding 6.
If we continue this pattern, we can find the missing numbers:
219 + 3 = 222
222 + 6 = 228
228 + 3 = 231
231 + 6 = 237
Hence, the missing numbers in the second part of the sequence are: 222, 228, 231, 237.