# The ordered pairs (1,36), (2, 49), (3,64). (4, 81). and (5, 100) represent a function. What is a rule that represents this function?

Jan 8, 2017

Rule is ${n}^{t h}$ ordered pair represents $\left(n , {\left(n + 5\right)}^{2}\right)$

#### Explanation:

In the ordered pairs $\left(1 , 36\right) , \left(2 , 49\right) , \left(3 , 64\right) . \left(4 , 81\right)$. and $\left(5 , 100\right)$, it is observed that

(i) first number starting from $1$ is in arithmetic series in which every number increases by $1$, i.e. $d = 1$

(ii) second number are squares and starting from ${6}^{2}$, it goes on to ${7}^{2}$, ${8}^{2}$, ${9}^{2}$ and ${10}^{2}$. Observe that $\left\{6 , 7 , 8 , 9 , 10\right\}$ to increase by $1$.

(iii) Hence while first part of first ordered pair starts from $1$, its second part is ${\left(1 + 5\right)}^{2}$

Hence the rule that represents this function is that

${n}^{t h}$ ordered pair represents $\left(n , {\left(n + 5\right)}^{2}\right)$