Three circles are concentric as in the diagram given below. If a fourt

Let’s analyze the sequence: 10, 5, 2.5.
The pattern is that each term is half of the previous term:
10 / 2 = 5
5 / 2 = 2.5

Following this pattern, the number for the fourth innermost circle should be half of the number for the third circle:
2.5 / 2 = 1.25

However, the options provided are 8, 7, 3, 1, which are all integers. This indicates that either the given sequence of numbers (10, 5, 2.5) or the options are incorrect, or the intended pattern leads to one of the integer options.

Let’s consider if there’s a different pattern that could lead to one of the integer options from starting values near 10 and 5. A common pattern type involves differences between consecutive terms.
Differences: 10 – 5 = 5. 5 – 2.5 = 2.5. The differences are 5, 2.5. This suggests a pattern where the difference is halved each time, leading to the next term being 2.5 – 1.25 = 1.25. This still leads to 1.25.

Let’s assume there is a typo in the number 2.5, and it was intended to be an integer that fits a pattern leading to one of the options. Let’s look at the options for the fourth term: 8, 7, 3, 1.
Let’s test if the sequence 10, 5, N3, N4 fits a simple integer pattern where N4 is one of the options.
Consider the sequence 10, 5, N3, 1 (Option D). Differences: 10-5=5, 5-N3, N3-1.
If the differences follow an arithmetic progression, say decreasing by 2: 5, 3, 1.
If the differences are 5, 3, 1, then:
10 – 5 = 5 (correct)
5 – 3 = 2. So, N3 should be 2.
2 – 1 = 1. So, N4 should be 1.
This forms the sequence 10, 5, 2, 1, where the differences are -5, -3, -1, which is an arithmetic progression of differences with common difference +2.

This pattern (differences -5, -3, -1) strongly suggests that the number for the third circle was intended to be 2, not 2.5, and the number for the fourth circle is 1. Assuming 2.5 is a typo for 2, the pattern holds and leads to option D.