In the sequence 2, 6, 12, 20, 30, what is the next number in the series? Explain the pattern.
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Let us do this step by step:
1) First, the differences between each consecutive number:
2 to 6: difference of 4
6 to 12: difference of 6
12 to 20: difference of 8
20 to 30: difference of 10
2) Now, we can see that the difference itself is also increasing by 2 each time:
4, 6, 8, 10
3) According to the pattern so far, the difference should be 12 this time.
4) So to get the next number, we once again add 12 to the number before:
30 + 12 = 42
5) Let’s now see the sequence in its entirety to check our answer:
2, 6, 12, 20, 30, 42
The pattern in this sequence is that each subsequent number is gotten by adding an incremental odd number to the anterior number.
In detail:
2 + 4 = 6
6 + 6 = 12
12 + 8 = 20
20 + 10 = 30
30 + 12 = 42
The next number in the sequence would thus be 42.
The differences between each consecutive number:
2 to 6 is 4
6 to 12 is 6
12 to 20 is 8
20 to 30 is 10
we can see that the difference itself is also increasing by 2 each time:
According to the pattern so far, the difference should be 12 this time.
So to get the next number, we once again add 12 to the number before:
30 + 12 = 42
Let’s now see the sequence in its entirety to check our answer:
The next number in the sequence would thus be 42.
The differences between each consecutive number:
2 to 6 is 4
6 to 12 is 6
12 to 20 is 8
20 to 30 is 10
we can see that the difference itself is also increasing by 2 each time:
According to the pattern so far, the difference should be 12 this time.
So to get the next number, we once again add 12 to the number before:
30 + 12 = 42
Let’s now see the sequence in its entirety to check our answer:
From this we get the next number as 42
In 2 to 6 difference is 4
IN 6 TO 12 difference is 6
In 12 to 20 difference is 8
In 20 to 30 difference is 10
The difference between all the number is even so the difference between 30 and next number is 12
So that
30+12=42
The correct answer is 42