Question 9

The missing numbers in the below series would be
1 : 1, 8 : 4, 9 : 27, 64 : 16, 25 : 125, ? : ?, 49 : 343

Solution

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1st term - 1^2:1^3

2nd term - 2^3:2^2

3rd term - 3^2:3^3 ...and so on.

The missing term is 6^3:6^2

Alternate:

Let us assume n is the nth term of the series-

When n is odd, the term is $$n^2:n^3$$

When n is even, the term is $$n^3:n^2$$

For n = 1,

1:1

For n = 2,

8:4

For n = 3,

9:27

For n = 4

64:16

Similarly, for n = 6

216:36

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