Mathematics 2022 JAMB Past Questions - Question 28:  What is the nth term of the sequence 2, 6, 12, 20,…?

Correct Answer

C

Explanation

To find the nth term of the sequence 2, 6, 12, 20, ..., we can observe that each term is obtained by adding consecutive odd numbers starting from 1.The first term is 2, which is obtained by adding 1 to 1.The second term is 6, which is obtained by adding 1 to 3.The third term is 12, which is obtained by adding 1 to 3 and then adding 3 to 6.The fourth term is 20, which is obtained by adding 1 to 3, then adding 3 to 6, and finally adding 5 to 12.From this pattern, we can see that the nth term is obtained by adding consecutive odd numbers starting from 1 up to n-1, and then adding the result to the (n-1)th term.Therefore, the nth term of the sequence is given by the formula:nth term = (n-1)^2 + (n-1)Simplifying this expression, we get:nth term = n^2 - n + n - 1nth term = n^2 - 1Therefore, the nth term of the sequence 2, 6, 12, 20, ... is given by n^2 - 1.