Question

What will be the missing term marked with [?] in the circle?

• A. 10
• B. 15
• C. 32
• D. 12

Hint:

This sequence is a "geometric Fibonacci-type series" where each term is the product (instead of sum) of the two preceding terms: \( T_n = T_{n-1} \times T_{n-2} \).

Answer 1

The Correct Option is C

Step 1: List the sector numbers in order.
Reading the circle clockwise gives $1,\ 2,\ 2,\ 4,\ 8,\ -$
Step 2: Look for a link between three consecutive terms.
Instead of differences, test whether each term is built from the two terms before it.
Step 3: Check the product rule.
$1 \times 2 = 2$ gives the third term, and $2 \times 2 = 4$ gives the fourth term.
Step 4: Confirm with the next pair.
$2 \times 4 = 8$ gives the fifth term, so the rule term$_n = $ term$_{n-2} \times$ term$_{n-1}$ holds consistently.
Step 5: Apply the rule to the missing slot.
The sixth term must be $4 \times 8 = 32$.
Step 6: Match to the options.
The value $32$ matches option C.
\[ \boxed{32} \]