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?

Rule is ##n^(th)## ordered pair represents ##(n,(n+5)^2)##

In the ordered pairs ##(1,36), (2, 49), (3,64). (4, 81)##. and ##(5, 100)##, 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 ##{6,7,8,9,10}## to increase by ##1##.

(iii) Hence while first part of first ordered pair starts from ##1##, its second part is ##(1+5)^2##

Hence the rule that represents this function is that

##n^(th)## ordered pair represents ##(n,(n+5)^2)##