$\begin{aligned}
1 ^ { 2 } & = 1 \cdot 1 \
1 ^ { 2 } + 1 ^ { 2 } & = 1 \cdot 2 \
1 ^ { 2 } + 1 ^ { 2 } + 2 ^ { 2 } & = 2 \cdot 3
\end{aligned}$
A) $1 ^ { 2 } + 1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } = 3 \cdot 5$
B) $1 ^ { 2 } + 1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + 5 ^ { 2 } = 5 \cdot 8$
C) $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } = 2 \cdot 7$
D) $1 ^ { 2 } + 1 ^ { 2 } + 2 ^ { 2 } + 2 ^ { 2 } = 2 \cdot 5$

Question

Quizplus · Accepted Answer

The pattern in the given equations is that the sum of squares on the left equals the product of two consecutive Fibonacci numbers on the right. For choice A, $1^2 + 1^2 + 2^2 + 3^2 = 15$ and $3 \cdot 5 = 15$, which follows the pattern.

12=1⋅112+12=1⋅212+12+22=2⋅3\begin{aligned}1 ^ { 2 } & = 1 \cdot 1 \\1 ^ { 2 } + 1 ^ { 2 } & = 1 \cdot 2 \\1 ^ { 2 } + 1 ^ { 2 } + 2 ^ { 2 } & = 2 \cdot 3\end{aligned}1212+1212+12+22​=1⋅1=1⋅2=2⋅3​

$\begin{aligned}1 ^ { 2 } & = 1 \cdot 1 \\1 ^ { 2 } + 1 ^ { 2 } & = 1 \cdot 2 \\1 ^ { 2 } + 1 ^ { 2 } + 2 ^ { 2 } & = 2 \cdot 3\end{aligned}$