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What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
48
50
125
92
None of these
Let's break down the sequence:
- Starting with 2: Look at the pattern.
- From 2 to 5: The difference is 3.
- From 5 to 11: The difference is 6.
- From 11 to 23: The difference is 12.
- From 23 to 44: The difference is 21.
- From 44 to 77: The difference is 33.
Now, observe the differences: 3, 6, 12, 21, 33.
- Each difference increases according to the sequence: 3 (3x1), 6 (3x2), 12 (3x4), 21 (3x7), 33 (3x11).
- These multipliers (1, 2, 4, 7, 11) increase by adding consecutive prime numbers: 1+1=2, 2+2=4, 4+3=7, 7+4=11, etc.
Following this pattern, the next difference should be 3 multiplied by the next increase, which is 16 (11+5).
- Next difference: 3 * 16 = 48.
- Value after 77: 77 + 48 = 125.
- So, the next number is 125.
- Correct answer: Option 3 - 125.
The other options don't fit the pattern:
- Option 1 (48): Too small.
- Option 2 (50): Too small.
- Option 4 (92): Doesn't fit the pattern.
- Option 5 (None of these): Not applicable since 125 fits.
By: Parvesh Mehta ProfileResourcesReport error
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