(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 7?
Answers
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
Learn more:
like this make another magic square using the principle Arithmetic ...
https://brainly.in/question/18797312
In an A.P if sum of its first n terms is 3n square +5n and it's Kth term ...
https://brainly.in/question/8236011
Find 5number in a AP whose sum is 25and the sum of square is 135 ...
https://brainly.in/question/8196345
