Question

Find the odd option from series 28, 29, 60, 123, 736, 3685

• A. 29
• B. 736
• C. 3685
• D. 123

Hint:

To identify the pattern in rapidly growing series, look at the last few terms:
$736 \rightarrow 3685$ is roughly a $5$-fold increase ($736 \times 5 = 3680$).
$183 \rightarrow 736$ is roughly a $4$-fold increase.
This indicates the pattern is based on multiplying by $1, 2, 3, 4, 5$ in sequence.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A number series is a sequence of numbers that follows a specific logical or mathematical pattern.
To find the odd or incorrect number in a series, we must analyze the mathematical relationships between successive terms to identify the consistent underlying pattern.

Step 2: Detailed Explanation:
Let us analyze the relationships between successive terms in the given sequence:
Sequence: $28, 29, 60, 123, 736, 3685$.
Let $T_1 = 28$.
Let us test a multiplicative-additive sequence pattern:
- Term 1 to Term 2: \[ T_2 = T_1 \times 1 + 1 = 28 \times 1 + 1 = 29 \] This matches the second term.
- Term 2 to Term 3: \[ T_3 = T_2 \times 2 + 2 = 29 \times 2 + 2 = 58 + 2 = 60 \] This matches the third term.
- Term 3 to Term 4:
Following this pattern ($T_n = T_{n-1} \times (n-1) + (n-1)$), the fourth term should be: \[ T_4 = T_3 \times 3 + 3 = 60 \times 3 + 3 = 180 + 3 = 183 \] However, the fourth term in the series is written as 123.
Let us verify if our proposed pattern makes the rest of the series correct if we replace $123$ with the hypothetical value $183$:
- Term 4 to Term 5: \[ T_5 = 183 \times 4 + 4 = 732 + 4 = 736 \] This matches the fifth term ($736$) perfectly.
- Term 5 to Term 6: \[ T_6 = 736 \times 5 + 5 = 3680 + 5 = 3685 \] This matches the sixth term ($3685$) perfectly.
This confirms that the pattern is correct.
The term $123$ is incorrect and disrupts the logical flow of the series; it should be replaced by $183$.

Step 3: Final Answer:
The odd number in the series is 1
Therefore, the correct option is (D).