Question

ഈ ശ്രേണിയുടെ അടുത്ത സംഖ്യ ഏത് ? 1, 2,5, 16, 65,........

• A. 326
• B. 271
• C. 196
• D. 131

Answer 1

Answer:

A. 326

Let’s look at the pattern:

Series: 1, 2, 5, 16, 65, ?

Step 1: Check pattern

Look at differences:

• 2 − 1 = 1

• 5 − 2 = 3

• 16 − 5 = 11

• 65 − 16 = 49

So differences are:
1, 3, 11, 49

Now check pattern in differences:

• $1 = (1^2)$

• $3 = (2^2 - 1)$

• $11 = (3^2 + 2)$

• $49 = (7^2)$

Not consistent directly, so try another approach:

Pattern relation

Each term:

• $1 = (1^2)$

• $2 = (1^2 + 1)$

• $5 = (2^2 + 1)$

• $16 = (3^2 + 7)$

• $65 = (4^2 + 49)$

Better pattern:

Check ratio idea:

• 1 × 1 + 1 = 2

• 2 × 2 + 1 = 5

• 5 × 3 + 1 = 16

• 16 × 4 + 1 = 65

So rule:

Multiply by increasing number and add 1

Next term

$65 \times 5 + 1 = 325 + 1 = 326$

Final Answer: 326