Question

Based on the given pattern find the next term of the given series: 5, 6, 16, 57, 244, 1245, ?

• A. 7506
• B. None of these
• C. 5500
• D. 4047

Hint:

In number series, look for operations of the form “multiply by $n$ then add $n^2$” or similar compound patterns.

Answer 1

The Correct Option is A

Step 1: Check the pattern of growth.
Observe each term:
$5 \to 6$: $5 \times 1 + 1 = 6$
$6 \to 16$: $6 \times 2 + 4 = 16$
$16 \to 57$: $16 \times 3 + 9 = 57$
$57 \to 244$: $57 \times 4 + 16 = 244$
$244 \to 1245$: $244 \times 5 + 25 = 1245$
Step 2: Generalize the rule.
Next term $=$ (Previous term $\times n$) $+ n^2$, where $n$ is the step number.
Step 3: Apply for the next term.
Here $n=6$:
$1245 \times 6 + 36 = 7470 + 36 = 7506$
\boxed{\text{Next term of the series is } 7506}