Question

Which of the following numbers will replace the question mark (?) in the given series? 13, 21, 33, 54, 91,?

• A. 183
• B. 162
• C. 175
• D. 153

Answer 1

Answer:

D. 153

The number that will replace the question mark (?) in the series is 153.

The series follows a double-difference pattern where the secondary differences are perfect squares:

1. Find the first layer of differences between consecutive terms:

• $21 - 13 =$ $8$

• $33 - 21 =$ $12$

• $54 - 33 =$ $21$

• $91 - 54 =$ $37$

2. Find the second layer of differences (the difference between the differences):

• $12 - 8 =$ $4$ (which is $2^2$)

• $21 - 12 =$ $9$ (which is $3^2$)

• $37 - 21 =$ $16$ (which is $4^2$)

3. Calculate the missing value:
Following the square pattern ($2^2, 3^2, 4^2$), the next secondary difference must be $5^2 = \mathbf{25}$.

• Add this to the last difference: $37 + 25 = \mathbf{62}$

• Add this target difference to the last term of the main series: $91 + 62 = \mathbf{153}$

Final Answer

The next number in the sequence is 153.