JAMB Mathematics 2013 Paper

Concept:Each term is a fraction whose numerator and denominator follow simple linear patterns based on the position $n$.Explanation:Write the given terms in terms of $n$:For $n = 1$, term is $\frac{4}{2}$.For $n = 2$, term is $\frac{7}{3}$.For $n = 3$, term is $\frac{10}{4}$.For $n = 4$, term is $\frac{13}{5}$.The numerators are $4, 7, 10, 13$, increasing by $3$ each time.So numerator $= 3n + 1$.The denominators are $2, 3, 4, 5$, increasing by $1$ each time.So denominator $= n + 1$.Thus the $n^{th}$ term is:$$T_n = \frac{3n + 1}{n + 1}$$Check for $n = 1$:$$T_1 = \frac{3(1)+1}{1+1} = \frac{4}{2}$$This matches the first term, so the formula is correct.Answer:Option B: $\frac{3n+1}{n+1}$