Express the set A= 1,7,17,31,49 in set builder form

Step-by-step solution

The given set is A = 1, 7, 17, 31, 49 . We observe the pattern of the elements: For n = 1 : 2(1)^2 - 1 = 2 - 1 = 1 For n = 2 : 2(2)^2 - 1 = 8 - 1 = 7 For n = 3 : 2(3)^2 - 1 = 18 - 1 = 17 For n = 4 : 2(4)^2 - 1 = 32 - 1 = 31 For n = 5 : 2(5)^2 - 1 = 50 - 1 = 49 The elements follow the rule x = 2n^2 - 1 for n 1, 2, 3, 4, 5 . This corresponds to the condition n N and n 5 . Answer: x x=2 n^2-1 . , where n N and .n 5