Question

Look at the series. What number should come next?5, 9, 25, 61, ?, 225.

Answer 1

Answer:

The required number is 125.

Step-by-step explanation:

Given series,

5 , 9 , 25 , 61 , ? , 225

We've to find the logic in the given series.

Let's take the first four terms.

5 , 9 , 25 , 61

• 9 - 5 = 4
• 25 - 9 = 16
• 61 - 25 = 36

4, 16 and 36 are perfect squares.

• 4 = 2²
• 16 = 4²
• 36 = 6²

They are squares of even numbers.

So,

next term = preceding term + square of even number

• first term = 5
• second term = 5 + 2² = 9
• third term = 9 + 4² = 25
• fourth term = 25 + 6² = 61
• fifth term = 61 + 8² = 61 + 64 = 125
• sixth term = 125 + 10² = 225

Therefore, the required number is 125.

Answer 2

Answer:

5, 9, 61, 125, 225

Step-by-step explanation:

Followed series is

5 + 2² = 5 + 4 = 9

9 + 4² = 9 ÷ 16 = 25

25 + 6² = 25 + 36 = 61

61 + 8²= 61 + 64 = 125

125 + 10² = 125 + 100 = 225