# How do you find the first five terms given a_1=3/4, a_(n+1)=(n^2+1)/n*a_n?

Jan 13, 2017

Sequence is $\left\{\frac{3}{4} , \frac{3}{2} , \frac{15}{4} , \frac{25}{2} , \frac{425}{8} , \ldots \ldots \ldots \ldots\right\}$

#### Explanation:

As ${a}_{1} = \frac{3}{4}$

${a}_{2} = {a}_{1 + 1} = \frac{{1}^{2} + 1}{1} \cdot {a}_{1} = 2 \cdot \frac{3}{4} = \frac{3}{2}$

${a}_{3} = {a}_{2 + 1} = \frac{{2}^{2} + 1}{2} \cdot {a}_{2} = \frac{5}{2} \cdot \frac{3}{2} = \frac{15}{4}$

${a}_{4} = {a}_{3 + 1} = \frac{{3}^{2} + 1}{3} \cdot {a}_{3} = \frac{10}{3} \cdot \frac{15}{4} = \frac{25}{2}$

${a}_{5} = {a}_{4 + 1} = \frac{{4}^{2} + 1}{4} \cdot {a}_{3} = \frac{17}{4} \cdot \frac{25}{2} = \frac{425}{8}$

and sequence is $\left\{\frac{3}{4} , \frac{3}{2} , \frac{15}{4} , \frac{25}{2} , \frac{425}{8} , \ldots \ldots \ldots \ldots\right\}$