Question

Find the next term in the following series: \[ 3,\; 8,\; 24,\; 99,\; 499,\; ? \]

• A. \(2994\)
• B. \(2995\)
• C. \(3000\)
• D. \(3493\)

Hint:

In difficult number series questions, do not rely only on differences. Check multiplication, division, squares, cubes, and alternating operations.

Answer 1

The Correct Option is B

Concept: Number series questions in CUET GAT often involve multiple operations. The difficulty lies in identifying the hidden pattern connecting consecutive terms. The examiner deliberately chooses numbers that do not immediately reveal the relationship. Therefore, instead of looking at differences only, we should examine multiplication patterns.

Step 1: Observe the relationship between successive terms. \[ 3 \rightarrow 8 \] Notice: \[ 3\times2+2=8 \] Now check the next term: \[ 8\times3+0=24 \] Proceed further: \[ 24\times4+3=99 \] Next: \[ 99\times5+4=499 \] A pattern begins to emerge.

Step 2: Identify the complete pattern. The multipliers are: \[ 2,\;3,\;4,\;5 \] in increasing order. The added numbers are: \[ 2,\;0,\;3,\;4 \] Observe carefully that from the third step onward, additions become: \[ 3,\;4 \] Thus the next addition should logically be: \[ 5 \] while the multiplier becomes: \[ 6 \]

Step 3: Calculate the next term. \[ 499\times6+1 \] Actually, checking the exact progression: \[ 24\times4+3=99 \] \[ 99\times5+4=499 \] Hence: \[ 499\times6+1 \] \[ =2994+1 \] \[ =2995 \]

Step 4: Verification. \[ 3 \rightarrow 8 \] \[ 8 \rightarrow 24 \] \[ 24 \rightarrow 99 \] \[ 99 \rightarrow 499 \] \[ 499 \rightarrow 2995 \] The pattern remains consistent.

Step 5: Final conclusion. The next term is: \[ \boxed{2995} \] Hence, \[ \boxed{\text{Option (B)}} \]