What should come in place of ‘?’ in the given series? 111, 223, 449, 903, 1813, ?
3635
To solve a number series, look for a rule that connects each term to the one before it. Here the terms grow to roughly double each step, so a good hypothesis is a recursive rule of the form "multiply by 2 and add something."
Step 1 — find the added amount. Test the pattern next = previous × 2 + odd number, where the added odd number increases by 2 each time:
- 111 × 2 + 1 = 223
- 223 × 2 + 3 = 449
- 449 × 2 + 5 = 903
- 903 × 2 + 7 = 1813
The rule fits every given term, and the added values 1, 3, 5, 7 form a neat sequence of consecutive odd numbers, confirming that the rule is correct rather than a coincidence.
Step 2 — extend the pattern. The next odd number to add is 9, so the missing term is 1813 × 2 + 9 = 3626 + 9 = 3635.
The distractors are designed to trap common errors: 3536 is a digit-transposition of the answer, 3630 and 3036 arise from adding the wrong constant or from a slip in the doubling. Only 3635 satisfies the ×2 + (next odd number) rule. The correct answer is 3635.
Similar Questions
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What should come in place of '?' in the given series?
39 52 65 78 91 ?
Important Questions from Sequence & Series
Which of the following options should come in place of the question mark (?) in the given series based on the English alphabetical order?
SHK, WLO, APS, ETW,?
Which of the following options should come in place of the question mark (?) in the given series based on the English alphabetical order?
EGI, KMO, QSU, WYA,?
Which of the following options should come in place of the question mark (?) in the given series?
14 15 18 23 30?
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
What should come in place of the question mark (?) in the given series based on the English alphabetical order?
TAW VCY XEA ZGC ?
