Find the next term in the alphanumeric series: Z3, B8, F24, L48, T120…

The correct answer is Option (3) → D168

1. Analyzing the Letter Pattern:

We look at the positions of the letters in the English alphabet ($A=1, B=2, \dots, Z=26$):

• Z (26)
• B (2) — (26 + 2 = 28; $28 - 26 = 2$) $\rightarrow$ Difference of +2
• F (6) — ($2 + 4 = 6$) $\rightarrow$ Difference of +4
• L (12) — ($6 + 6 = 12$) $\rightarrow$ Difference of +6
• T (20) — ($12 + 8 = 20$) $\rightarrow$ Difference of +8

The differences follow the sequence: $+2, +4, +6, +8$. The next difference should be +10.

• $20 (\text{T}) + 10 = 30$
• In the circular alphabet ($30 - 26 = 4$), the $4^{th}$ letter is D.

2. Analyzing the Number Pattern:

The numbers in the series are: 3, 8, 24, 48, 120.

Notice that these numbers are all one less than the square of a prime number:

• $2^2 - 1 = 4 - 1 = \mathbf{3}$
• $3^2 - 1 = 9 - 1 = \mathbf{8}$
• $5^2 - 1 = 25 - 1 = \mathbf{24}$
• $7^2 - 1 = 49 - 1 = \mathbf{48}$
• $11^2 - 1 = 121 - 1 = \mathbf{120}$

The base numbers being squared are the prime numbers: 2, 3, 5, 7, 11.

The next prime number after 11 is 13.

• $13^2 - 1 = 169 - 1 = \mathbf{168}$

Conclusion:

By combining the next letter (D) and the next number (168), we get the term D168.