A series of diagrams of squares is shown below. Draw Diagram ${4}$. Copy and complete the followin

Question

A series of diagrams of squares is shown below. Draw Diagram ${4}$. Copy and complete the following table. DiagramNumber of squares ${1}$${1 + 1 \times 3 = 4}$ ${2}$${1 + 2 \times 3 = 7}$ ${3}$${1 + 3 \times 3 = 10}$ ${4}$ $\vdots$ ${10}$ Find an expression, in terms of ${N}$, for the number of squares for Diagram ${N}$. Diagram ${K}$ has ${64}$ squares. Find the value of ${K}$.

Accepted Answer

(a) L-shape with $9$ squares across the top and $5$ down the left, sharing the corner (b) Diagram $4$: $13$, Diagram $10$: $31$ (c) $3N+1$ (d) $K=21$

Diagram	Number of squares
\({1}\)	\({1 + 1 \times 3 = 4}\)
\({2}\)	\({1 + 2 \times 3 = 7}\)
\({3}\)	\({1 + 3 \times 3 = 10}\)
\({4}\)
\(\vdots\)
\({10}\)

Square Diagram Pattern: Number of Squares

Square Diagram Pattern: Number of Squares

Video Solution:

Solution:

Solution locked