Question

name: kara
algebraic patterns
geometric shapes

1. continue the pattern below for the 4th and 5th terms.

1 2 3 4
(geometric shapes pattern: diamonds and triangles)

1. write an algebraic expression for this pattern.

(partially visible text at bottom)

Explanation:

Step1: Analyze the pattern of diamonds

For term 1 (n=1), number of diamonds = 1.
For term 2 (n=2), number of diamonds = 2.
For term 3 (n=3), number of diamonds = 3.
So, for term n, number of diamonds = n.

Step2: Analyze the pattern of triangles

For term 1 (n=1), number of triangles = 3.
For term 2 (n=2), number of triangles = 3.
For term 3 (n=3), number of triangles = 3.
So, for term n, number of triangles = 3.

Step3: Continue the pattern for 4th and 5th terms

4th term (n=4):

• Diamonds: 4 (since n=4)
• Triangles: 3 (constant)

5th term (n=5):

• Diamonds: 5 (since n=5)
• Triangles: 3 (constant)

Step4: Write the algebraic expression

Let n be the term number.
Total number of shapes (diamonds + triangles) = number of diamonds + number of triangles = \( n + 3 \).
Or, if we consider each shape type:

• Diamonds: \( n \)
• Triangles: \( 3 \)

Answer:

1. 4th term: 4 diamonds and 3 triangles; 5th term: 5 diamonds and 3 triangles.
2. Algebraic expression (for total shapes): \( n + 3 \) (where \( n \) is the term number), or for diamonds: \( n \), for triangles: \( 3 \).