LUUKUL ULSC.
32 + 12 = 2 x 22 + 2
42 + 22 = 2 x 32 + 2
52 + 32 = 2 x 42 + 2
62 + 42 = 2 x 52 + 2
a) Write the next four lines in this pattern .
b) If we take three consecutive natural numbers , what is the relation between the sum of
the squares of the first and last numbers and the square of the middle number?
c) If we take the middle number among three consecutive natural numbers is x ,what will
be the other numbers ?
d) Write the general principle in the above pattern in algebra and explain it.
Answer:
a) 72+52=2*62+2
82+62=2*72+2
92+72=2*82+2
102+82=2*92+2