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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
