Question

Maria Louisa looks at a sequence of shapes and records the number of vertices in each of the shapes in the sequence. The first shape has 3 vertices, the second shape has 5 vertices, and the third shape has 7 vertices.

If Maria Louisa assumes that the number of vertices in the sequence of shapes follows the same pattern, how many vertices would she expect the twenty-first shape to have?

Answer 1

Explanation:

arithmetic sequence.

an = an-1 + c = a1 + (n-1)c

c is in our case 2 (every new shape has 2 more vertices).

we have a a1 = 3.

an = 3 + 2(n-1)

so,

a21 = 3 + 2(20) = 3 + 40 = 43

the 21st shadow will have 43 vertices.