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Question

Using the given pattern, find the missing numbers.
12+22+22=32
22+32+62=72
32+42+122=132
42+52+...2=212
52+...2+302=312
62+72+....2=....2.

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Solution

Given 12+22+22=32
22+32+62=72
32+42+122=132
Here, the pattern we can identify is that the third number is the product of first and second number.
Because, for 12+22+22=32
Here, the third number is 2=1×2
The same rule holds for the next two equations as well.
Similar way, the fourth term is 1 more than the third term.
Because, for 12+22+22=32
Here, the fourth term is 3=2+1
The same rule holds for the next two equation as well.
(i) Now for, 42+52+...2=212
Since, here third term is product of first terms .
That is third term is =4×5=20
Therefore, the given equation can be written as 42+52+202=212
(ii) Similar way for ,52+...2+302=312
Since, the third term (c=30) is product of first term (a=5) and second term (b=?).
Thus, c=ab
b=ca
=305
b=6
Hence, the given expression can be written as 52+62+302=312

(iii) For 62+72+....2=....2
Third term is product of first two terms.
That is third term =6×7=42
The fourth term is one more than the third term.
That is fourth term is=42+1=43
Therefore, the given expression is 62+72+422=432


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