Question

Find the missing series of 4, 27, 25, 343, 121

Answer 1

Step-by-step explanation:

Solution:

1^3 = 1

2^2 = 4

3^3 = 27

4^2 = 16

So,

5^3 = 125

6^2 = 36

7^3 = 343

the answer is 125.

Answer 2

Answer:

Required missing number is 2197.

Step-by-step explanation:

Given, series 4, 27, 25, 343, 121.

This is a problem of General inteligence part of Mathematics.

If we look it carefully then we can solve this problem easily.

Here all terms are maintaining a sequence.

$4 = {2}^{2} \\ 27 = {3}^{3} \\ 25 = {5}^{2} \\ 343 = {7}^{3} \\ 121 = {11}^{2}$

According to rule,

This is a series of odd numbers.

After 11,odd number will be 13.

So,next number $= {13}^{3} = 2197$

So, required missing number is 2197.

Some important Mathematics formulas:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

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