Notes: `1, 1/4, 1/9, 1/16, 1/25` Write an expression for the apparent nth term of the sequence. (assume that n begins with 1)

Friday, December 30, 2016

Numerator is always 1 while the denominator is a square number, thus we can write the sequence as follows

$\displaystyle\frac{{1}}{{{1}}^{{2}}},\frac{{1}}{{{2}}^{{2}}},\frac{{1}}{{{3}}^{{2}}},\frac{{1}}{{{4}}^{{2}}},\frac{{1}}{{{5}}^{{2}}},\ldots$

From this we see that the $\displaystyle{n}$ th terms is

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

Numerator is always 1 while the denominator is a square number, thus we can write the sequence as follows

$\displaystyle\frac{{1}}{{{1}}^{{2}}},\frac{{1}}{{{2}}^{{2}}},\frac{{1}}{{{3}}^{{2}}},\frac{{1}}{{{4}}^{{2}}},\frac{{1}}{{{5}}^{{2}}},\ldots$

From this we see that the $\displaystyle{n}$ th terms is

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

Notes