Question

21 1/3,16,12,9 what is the next number and how?​

Answer 1

Given data:

$21\frac{1}{3}, 16, 12, 9, ?$

To find:

The next term in the series.

Solution:

As clearly we find that there is no exact addition, or difference, as in Arithmetic progression here,

Let us try the geometric progression here.

$21\frac{1}{3}, 16, 12, 9, ? = \frac{64}{3}, 16, 12, 9, ?$

$Here, \frac{T_1}{T_2} =\frac{64/3}{16} = \frac{64}{3 x16} = \frac{4}{3} \\\\ \frac{T_2}{T_3} =\frac{16}{12} = \frac{4}{3} \\\\ \frac{T_3}{T_4} =\frac{12}{9} = \frac{4}{3}$            

As every ratio 'r' is same, they are in geometric progression.

So, on dividing every number with 'r', we get the next number. As in:

Here, r= 4/3. So, 1/r = 3/4

So, multiply a number with 3/4 to get the next number.

64/3 x 3/4 = 16

16 x 3/4 = 12

12 x 3/4 = 9

The next number in the series will be:

9 x 3/4 = 6 3/4 or 6.75

The series is 21 1/3, 16, 12, 9, 6 3/4 or 6.75

Learn more:

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