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?

1 Answer
Shwetank Mauria
Jan 8, 2017

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

Explanation:

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)#

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