What is the next number 2 7 8 3 12 9?
The Correct Answer and Explanation is:
Next number: 18
Sequence: 2, 7, 8, 3, 12, 9, ?
Let’s break the sequence into patterns:
Step 1: Separate into two alternating sequences
- Odd positions: 1st, 3rd, 5th → 2, 8, 12
- Even positions: 2nd, 4th, 6th → 7, 3, 9
Now analyze both sub-sequences:
Sequence A (Odd Positions): 2, 8, 12
Check how it progresses:
- 2 → 8 (difference of +6)
- 8 → 12 (difference of +4)
So the pattern is:
- +6, +4, …
It seems like the pattern is decreasing by 2 each time, so the next increment may be +2:
- 12 + 2 = 14
But this pattern doesn’t continue into the next term (since we only have three terms so far, it’s not reliable). Let’s double-check the Even Positions pattern.
Sequence B (Even Positions): 7, 3, 9
Check differences:
- 7 → 3 = -4
- 3 → 9 = +6
If the pattern alternates between -4 and +6, the next move would be -4 again:
- 9 → 5
But this leads to a disjoint with the other side. Try another approach.
Try pair-wise operation:
Let’s group numbers in pairs:
- (2, 7), (8, 3), (12, 9)
Check how each second number relates to the first:
- 2 + 5 = 7
- 8 – 5 = 3
- 12 + 5 = 17
So it alternates +5, -5, +5 — suggesting a -5 next:
- 17 – 5 = 12
But we have 9 as the 6th term, not 17.
Let’s try a new approach.
Look at consecutive pairs:
Check how numbers change:
- 2 → 7 = +5
- 7 → 8 = +1
- 8 → 3 = -5
- 3 → 12 = +9
- 12 → 9 = -3
- So pattern: +5, +1, -5, +9, -3, ?
Let’s look at that sequence of differences:
+5, +1, -5, +9, -3
Pattern of differences: Alternating positive and negative values that reduce or increase:
Observe:
- +5 (→ +1 → -5)
- then (+9 → -3 → ?)
Seems like each positive increase is getting larger by 4:
- +1 to +5 → increase of 4
- +5 to +9 → increase of 4
So next should be +13
And negatives go:
- -5 → -3 → -1 (increasing by +2 each time)
So, based on alternating pattern:
Last difference was -3, next should be +13:
- 9 + 13 = 22
✅ Final Answer: 22
Explanation
To find the next number in the sequence 2, 7, 8, 3, 12, 9, we analyze the changes between terms. First, we examine the differences between each pair of consecutive numbers:
- 2 → 7 = +5
- 7 → 8 = +1
- 8 → 3 = -5
- 3 → 12 = +9
- 12 → 9 = -3
These differences form the new sequence: +5, +1, -5, +9, -3.
This pattern reveals alternating positive and negative changes, with the positive values increasing each time:
- +1 → +5 → +9: each time, the increase is +4
Thus, the next positive value should be: +9 + 4 = +13
The negative changes are: -5 → -3
This increases by +2 (i.e., the negative number becomes less negative), suggesting the next negative value would be -1.
But since we just had a -3 (negative), and the sequence alternates between positive and negative differences, the next difference should be a positive one — which we’ve predicted to be +13.
So, the last number in the sequence is 9. Add 13 to it:
- 9 + 13 = 22
Therefore, the next number in the sequence is 22.
This sequence showcases a pattern of alternating increasing and decreasing values, governed by arithmetic increments and decrements in their own sub-patterns. Recognizing the alternating pattern and tracking the rate of increase or decrease helps us identify the logical next step.
