What will be the missing term marked with [?] in the circle?
Show Hint
This sequence is a "geometric Fibonacci-type series" where each term is the product (instead of sum) of the two preceding terms: \( T_n = T_{n-1} \times T_{n-2} \).
Step 1: Understanding the Question:
We need to find the missing number represented by [?] in the sector of the circle by identifying the mathematical relationship between the numbers in adjacent sectors.
Step 2: Detailed Explanation:
Let us list the numbers in the sectors starting from the top-right and moving in a clockwise direction:
- Sector 1: 1
- Sector 2: 2
- Sector 3: 2
- Sector 4: 4
- Sector 5: 8
- Sector 6: ?
Let us look at the relationship between successive terms in this sequence:
- The third term is the product of the first and second terms:
\[
1 \times 2 = 2
\]
- The fourth term is the product of the second and third terms:
\[
2 \times 2 = 4
\]
- The fifth term is the product of the third and fourth terms:
\[
2 \times 4 = 8
\]
Following this multiplication-progression rule, the sixth term (the missing number) must be the product of the fourth and fifth terms:
\[
4 \times 8 = 32
\]
Thus, the missing number is 32.
