Question

How many triangles would be in the 57th figure?

Figure One:

3 triangles

Figure two:

5 triangles

FIgure three:

7 triangles

Answer 1

115

Explanation:

Consider the sequence of triangles

3, 5, 7

There is a common difference between consecutive terms, that is

d = 7 - 5 = 5 - 3 = 2

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = 2, thus

`a_(57)` = 3 + (56 × 2) = 3 + 112 = 115