What is the missing number in the following sequence: 1 , 16 , _ , 100, 169

Solution:

Given, the sequence is 1, 16, ____, 100, 169

We have to find the missing number in the sequence.

Let the missing number be m.

From the series,

1 = 1 × 1

16 = 4 × 4

m² = m × m

100 = 10 × 10

169 = 13 × 13

After expansion of the series, we find that 

4 - 1 = 3

13 - 10 = 3

Similarly, m - 4 = 3

m = 4 + 3

m = 7

10 - m = 3

10 - 3 = m

m = 7

So,m² = m × m

7 × 7 = 49

Therefore, the missing number is 49.

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What is the missing number in the following sequence: 1 , 16 , _ , 100, 169

Summary:

The missing number in the following sequence: 1 , 16 , _ , 100, 169 is 49.