# How do you write the first five terms of the sequence a_n=3^n/(n!)?

Apr 24, 2017

$3 , \frac{9}{2} , \frac{9}{2} , \frac{27}{8} , \frac{81}{40}$

#### Explanation:

$\text{evaluate for } n = 1 , 2 , 3 , 4 , 5$

$\Rightarrow {a}_{1} = \frac{3}{1} = 3$

$\Rightarrow {a}_{2} = {3}^{2} / \left(2 \times 1\right) = \frac{9}{2}$

$\Rightarrow {a}_{3} = {3}^{3} / \left(3 \times 2 \times 1\right) = \frac{27}{6} = \frac{9}{2}$

$\Rightarrow {a}_{4} = {3}^{4} / \left(4 \times 3 \times 2 \times 1\right) = \frac{81}{24} = \frac{27}{8}$

$\Rightarrow {a}_{5} = {3}^{5} / \left(5 \times 4 \times 3 \times 2 \times 1\right) = \frac{243}{120} = \frac{81}{40}$