The numerical series given below follows a particular sequence. Fill in the missing elements.

16 23 37 65 121 ? 457 ?

Looking at the series: 16, 23, 37, 65, 121, ?, 457, ?

To find the pattern, let's check the differences between consecutive terms:

From → To	Calculation	Difference
16 → 23	23 - 16	7
23 → 37	37 - 23	14
37 → 65	65 - 37	28
65 → 121	121 - 65	56

The differences are: 7, 14, 28, 56

Notice that each difference is double the previous one:

• $7 \times 2 = 14$
• $14 \times 2 = 28$
• $28 \times 2 = 56$

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Continuing this pattern:

The next difference = $56 \times 2 = 112$

So the 6th term = $121 + 112 = 233$

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To verify and find the last term, the next difference = $112 \times 2 = 224$

The 7th term should be = $233 + 224 = 457$ ✓ (This matches the given term, confirming our pattern is correct)

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For the 8th term:

The next difference = $224 \times 2 = 448$

So the 8th term = $457 + 448 = 905$

The missing terms are 233 and 905.

Answer: Option 4