(6) Fill up the empty cells of the given square such that the
numbers in each row and column form arithmetic
sequences
What if we use some other numbers instead of 1,4,
28 and 72
016
nus the alme
7
28 ow look
Answers
Answer:
Explanation:
First: solve the common difference of term 1.......4.in the equation of xn-x1÷n-1 .
Like this, d=4-1÷4-1=3÷3=1
And add 1+1=2
Like that do all teems and you willbget your answer .Total answer is
Given : A square having some numbers
to find : fill empty cells such that the numbers in each row and column form arithmetic sequences:
Solution:
1 x x 4
x x x x
x x x x
7 x x 28
1st row
first term = 1 , 4th term = 4
=> 4 = 1 + 3d => d = 1
Hence 1st row
1 2 3 4
4th row
first term = 7 , 4th term = 28
=> 28 = 7 + 3d => d = 7
Hence 1st row
7 14 21 28
1st column
first term = 1 , 4th term = 7
=>7 = 1 + 3d => d = 2
Hence 1st row
1
3
5
7
4th column
first term = 4 , 4th term = 28
=> 28 = 4 + 3d => d = 8
Hence 1st row
4
12
20
28
1 2 3 4
3 x x 12
5 x x 20
7 14 21 28
solve similarly 2nd row
3 6 9 12
3rd row
5 10 15 20
no need to solve columns but can be verified
1 2 3 4
3 6 9 12
5 10 15 20
7 14 21 28
if 7 & 8 are not given
Simplest square can be formed is
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 7
one more example :
1 3 5 7
2 4 6 8
3 5 7 9
4 6 8 10
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