Question: The rule for nth term of a pattern is 2n2 + 1. Find the first four terms of the pattern starting from 1.
A ) 1, 3, 9, and 19. B ) 3, 9, 19, and 33. C ) 3, 9, 18, and 33. D ) 3, 8, 19, and 32.
Steps to derive
1 The rule for nth term of the pattern is 2n2 + 1. [Given.]
2 To get the first term, substitute n = 1 in 2n2 + 1 = 2(1)2 + 1 = 2 + 1 = 3 To get the second term, substitute n = 2 in 2n2 + 1 = 2(2)2 + 1 = 8 + 1 = 9 To get the third term, substitute n = 3 in 2n2 + 1 = 2(3)2 + 1 = 18 + 1 = 19 To get the fourth term, substitute n = 4 in 2n2 + 1 = 2(4)2 + 1 = 32 + 1 = 33.
3 So, the first four terms starting from 1 is 3, 9, 19, and 33.
