Question

The difference between the second and the first term of a sequence defined by $t_n=\frac{n^3}{4n+1}$

• A. $\frac{31}{45}$
• B. $\frac{49}{45}$
• C. $\frac{4}{45}$
• D. $\frac{11}{45}$

Answer 1

The correct option is A $\frac{31}{45}$

Given: $t_n=\frac{n^3}{4n+1}$
∴ First term of the sequence, $t_1=\frac{(1{)}^3}{(4\times 1)+1}=\frac{1}{5}$
∴ Second term of the sequence, $t_2=\frac{(2{)}^3}{(4\times 2)+1}=\frac{8}{9}$

Thus, the difference between the second and first term $=\frac{8}{9}-\frac{1}{5}=\frac{40-9}{45}=\frac{31}{45}$

Hence, the correct answer is option (1).