ccss.hsa-sse.a.1.q.a1.bqf.3 - Which expression represents the relationship between the step number, n, and the total number of small squares in the pattern?

Which expression represents the relationship between the step number, n, and the total number of small squares in the pattern?

106 viewed last edited 2 years ago

ccss.hsa-sse.a.1.q.a1.bqf.3 ccss.hsf-bf.a.1.a.q.a1.bqf.3 ccss.hsf-if.a.2.q.a1.bqf.3 hsa-sse.a.1 hsf-bf.a.1.a hsf-if.a.2 relationship between step number and number of squares building quadratic functions from geometric patterns

Anonymous

A. n^{2} +1.

B. n^{2} - 1

C. n^{2} - n

D. n^{2} + n

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

Let n be the step number,

Step 1 has 2 squares, step 2 had 6 squares, step 3 has 10 squares.

The equation which satisfies this situation is n^{2} + 1.

When we plug in n = 1, we get 1^{2}+1 = 2. These are the number of squares in step 1.

When we plug in n = 2, we get 2^{2}+1 = 5. These are the number of squares in step 2.

When we plug in n = 3, we get 3^{2} + 1 = 10. These are the number of squares in step 3.