The simplest pattern that your teacher is most likely to want is:
U{n} = (n + 5)² for n = 1, 2, 3, 4
ie each term is the square of the next whole number starting with 6:
{36, 49, 64, 81} = {6², 7², 8², 9²}
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81
Reducing squares 100 = 10² 81 = 9² 64 = 8² 49 = 7² 36 = 6² so next is 25 = 5² ---------------------------------- For the given pattern the nth term (n = 1 to 5) is given by: t(n) = n² - 22n + 121
Reducing squares 9 x 9 = 81 8 x 8 = 64 7 x 7 = 49 6 x 6 = 36 so next would be 5 x 5 = 25
These are square numbers. 81 = 9 x 9 64 = 8 x 8 49 = 7 x 7 36 = 6 x 6
25, 36, 49, 64, 81
Average= (36+49+64+81+100)/5 =330/5 =66
81
Reducing squares 100 = 10² 81 = 9² 64 = 8² 49 = 7² 36 = 6² so next is 25 = 5² ---------------------------------- For the given pattern the nth term (n = 1 to 5) is given by: t(n) = n² - 22n + 121
81
Reducing squares 9 x 9 = 81 8 x 8 = 64 7 x 7 = 49 6 x 6 = 36 so next would be 5 x 5 = 25
These are square numbers. 81 = 9 x 9 64 = 8 x 8 49 = 7 x 7 36 = 6 x 6
.... 49, 36, 25, 16, 9, 4 and 1
25, 36, 49, 64, 81
36, 49, 64, 81, 100
These are the square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81...
25 36 49 64 81
36, 49, 64 and 81