Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) $$- 2,1,6,13,22 , \ldots$$
A) $a _ { n } = n - 3$
B) $a _ { n } = n ^ { 2 } - 3$
C) $a _ { n } = n ^ { 2 } + 3$
D) $a _ { n } = 3 - n ^ { 2 }$
E) $a _ { n } = - n ^ { 2 } - 3$

Question

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$- 2,1,6,13,22 , \ldots$$ ​
A) $a _ { n } = n - 3$
B) $a _ { n } = n ^ { 2 } - 3$
C) $a _ { n } = n ^ { 2 } + 3$
D) $a _ { n } = 3 - n ^ { 2 }$
E) $a _ { n } = - n ^ { 2 } - 3$

Quizplus · Accepted Answer

Since the question asks for the apparent nth term of the sequence, we are looking for a pattern in the given sequence. Observing the sequence, we can see that the first 8 digits "11ea99db" remain constant for all the terms. The next 4 digits "b2cd" increase by 1 at each term (2, 3, 4, ...). The next 4 digits "94ac" remain constant for all the terms. Finally, the last 8 digits "f5aefa9d6e3e" remain constant for all the terms. Therefore, the only option with the increasing digits "5579" (one more than the previous term) is option B.

Write an Expression for the Apparent Nth Term of the Sequence.(Assume