1. **Stating the problem:** We are given a pattern of equations: $1 + 4 = 5$ $2 + 5 = 12$ $3 + 6 = 21$ $8 + 11 = ?$ We need to find the value of $8 + 11$ based on the pattern. 2. **Observing the pattern:** The sums on the right side are not the usual sums of the left side numbers. Let's analyze the pattern: - For $1 + 4 = 5$, the normal sum is $5$. - For $2 + 5 = 12$, the normal sum is $7$, but the result is $12$. - For $3 + 6 = 21$, the normal sum is $9$, but the result is $21$. 3. **Finding the rule:** Notice that: - $1 \times 4 + 1 = 4 + 1 = 5$ - $2 \times 5 + 2 = 10 + 2 = 12$ - $3 \times 6 + 3 = 18 + 3 = 21$ So the pattern is: $$a + b = a \times b + a$$ 4. **Applying the rule to $8 + 11$:** $$8 + 11 = 8 \times 11 + 8 = 88 + 8 = 96$$ **Final answer:** $96$