Question

The figures below show a pattern.





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Find the expression that could be used to determine the number of squares in the nth figure.

Answer 1

Answer:

$a_{n}$ = 3n + 1

Step-by-step explanation:

Th number of squares in each figure is

4, 7, 10, ....

The terms have a common difference, that is

7 - 4 = 10 - 7 = 3

The number of squares in the n th figure is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 4 and d = 3, thus

$a_{n}$ = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1