JAMB Mathematics 2021 Paper

Concept:The sequence follows a quadratic pattern where each term can be expressed as a function of its position $n$, specifically the sum of squares and the natural numbers.Explanation:The given sequence is $2, 6, 12, 20, \dots$.Observe that each term can be written as $n^2 + n = n(n+1)$.Check the first term: for $n = 1$, $1^2 + 1 = 1 + 1 = 2$.Check the second term: for $n = 2$, $2^2 + 2 = 4 + 2 = 6$.Check the third term: for $n = 3$, $3^2 + 3 = 9 + 3 = 12$.Check the fourth term: for $n = 4$, $4^2 + 4 = 16 + 4 = 20$.Since all given terms match $n^2 + n$, this is the correct general term.The expression $n^2 + n$ corresponds to option C.Answer:The n-th term is $n^2 + n$, which is option C.