# How do you write the expression for the nth term of the sequence given 1, 1/4, 1/9, 1/16, 1/25,...?

Feb 24, 2017

${a}_{n} = \frac{1}{n} ^ 2$

#### Explanation:

$n : 1 , 2 , 3 , 4 , 5. . .$
${a}_{n} : 1 , \frac{1}{4} , \frac{1}{9} , \frac{1}{16} , \frac{1}{25.} . .$

${1}^{2} = 1 , {2}^{2} = 4 , {3}^{2} = 9$, etc.

$n : 1 , 2 , 3 , 4 , 5. . .$
${n}^{2} : 1 , 4 , 9 , 16 , 25. . .$

$n : 1 , 2 , 3 , 4 , 5. . .$

$\frac{1}{n} ^ 2 : \frac{1}{1} , \frac{1}{4} , \frac{1}{9} , \frac{1}{16} , \frac{1}{25.} . .$

$\therefore {a}_{n} = \frac{1}{n} ^ 2$