What is the next number in the sequence $225, 100, 36, 9, 1, ?$

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- 7

- 6

- 1

answer is C.

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Detailed Solution

Given,
The sequence is

225, 100, 36, 9, 1

First term,
225 = 15 × 15
Second term,
100 = 10 ×10
Third term,
36 = 6 × 6
Fourth term,
9 = 3 × 3
Fifth term,
1 = 1 ×1
Now new sequence is,
15, 10, 6, 3, 1, …
From this sequence, we can see that:
15 – 10 = 5
10 – 6 = 4
6 – 3 = 3
3 – 1 = 2
We can see that consecutive numbers reduces continuously.
So, the root of the next element as,
1 – 1 = 0
Thus we also know that, the square of 0 is 0.
So, the next element of the sequence is 225, 100, 36, 9, 1, … is 0.
Correct option is 3.

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