How many dots will be in the next figure in this pattern?
1 3 6 10…
30
15
20
12
The pattern in this sequence is that each number increases by 2, then 3, then 4, and so on.
To find the number of dots in the next figure, we need to determine which group number the next figure belongs to.
1 + 2 = 3 (Group 1)
3 + 3 = 6 (Group 2)
6 + 4 = 10 (Group 3)
We can see that the next figure will belong to Group 4, so we need to add 5 more dots to reach the next total.
10 + 5 = 15
Therefore, the number of dots in the next figure will be 15. Answer: 15.
To find the number of dots in the next figure in this pattern, we need to look for the pattern in the given sequence: 1, 3, 6, 10.
If we observe closely, we can see that each number in the sequence is the sum of consecutive positive integers.
1 = 1
3 = 1 + 2
6 = 1 + 2 + 3
10 = 1 + 2 + 3 + 4
So, the next pattern will be the sum of 1, 2, 3, 4, and 5:
1 + 2 + 3 + 4 + 5 = 15
Therefore, there will be 15 dots in the next figure in this pattern.
The answer is 15.
To determine the number of dots in the next figure in the given pattern, we need to identify the pattern or rule that governs how the numbers in the sequence are generated.
By examining the given sequence 1, 3, 6, 10..., we can observe that each number is obtained by adding the next consecutive number starting from 2.
Let's break it down:
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
Therefore, we can conclude that the pattern or rule is to add the next consecutive number starting from 2.
Now, let's apply this rule to find the next number in the sequence:
10 + 5 = 15
Hence, the next number in the sequence is 15.
Since the number in the sequence represents the number of dots in each figure, the next figure will have 15 dots.
Therefore, the correct answer is 15 dots.