Choose the correct alternative from the given options that will replace the question mark (?) in the following series:

7, 8, 18, 57, ?, 1165

232

The correct answer is Option (2) → 232

Analyzing the Pattern

By looking at the relationship between consecutive numbers, we can see a pattern of multiplying by an increasing integer and then adding that same integer:

• 1st term to 2nd term: $(7 \times 1) + 1 = 8$
• 2nd term to 3rd term: $(8 \times 2) + 2 = 18$
• 3rd term to 4th term: $(18 \times 3) + 3 = 57$

Calculating the Missing Number (?)

Following the established pattern, we multiply the fourth term by 4 and add 4:

• 4th term to 5th term: $(57 \times 4) + 4$
• $228 + 4 = \mathbf{232}$

Verification

Let's check if this value works for the final term in the series by multiplying by 5 and adding 5:

• 5th term to 6th term: $(232 \times 5) + 5$
• $1160 + 5 = \mathbf{1165}$ (Matches the series)

Conclusion: The missing number that replaces the question mark is 232.