"The ordered pairs (1,36), (2, 49), (3,64). (4,..." solved and explained

Raina Cole

Answered question

2023-01-06

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?

Jason Ramirez

Beginner2023-01-07Added 3 answers

In the ordered pairs

(1, 36), (2, 49), (3, 64) . (4, 81)

. and

(5, 100)

, it is observed that
(i) first number starting from #1ZSK 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}

Consequently, the rule for this function is that

n^{t h}

ordered pair represents

(n, {(n + 5)}^{2})

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