BECE Mathematics 2021 Paper

Concept:The sequence is quadratic because the second differences between terms are constant.Explanation:First, find the differences between consecutive terms.$5-2=3$, $10-5=5$, and $17-10=7$.These first differences $3,5,7$ are not equal, so the sequence is not linear.Now find the differences of these first differences.$5-3=2$ and $7-5=2$.Since the second difference is constant $2$, the sequence follows a quadratic pattern.The next first difference after $7$ is $7+2=9$.So the $5$th term is $17+9=26$.The next first difference after $9$ is $9+2=11$.So the $6$th term is $26+11=37$.This pattern matches the general term $U_n=n^2+1$.Verify: $1^2+1=2$, $2^2+1=5$, $3^2+1=10$, and $4^2+1=17$.Thus, $U_5=5^2+1=26$ and $U_6=6^2+1=37$.Answer:The next two terms are $26, 37$, which is option C.