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Answer:

(n + 2)² + 6

Step-by-step explanation:

pattern 1:

Total squares = 15

3² + 6 = 16

Pattern 2:

Total squares = 22

4² + 6

Pattern 3:

Total squares = 31

5² + 6

Looking at the series,

There is an Increment of 1 in squared integer as the pattern increases; there is also a constant integer of 6

Hence, expressing the nth pattern in the form ;

(n + a)² + b

Where n is the nth pattern ; a = (Coefficient of n² in first pattern - 1) = (3 - 1) =2 ;

b = 6

Hence, we have ;

(n + 2)² + 6

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