Question

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?

Answer 1

1. In the first row differences between 1st and 4th terrm = 3

Position difference = 4 – 1 = 3

Common difference = 3/3 = 1

Arithmetic sequence 1, 2, 3,4

2. In the first coloumn Term difference = 7 – 1 = 6

Position difference = 4 – 1 = 3

Common difference = 6/3 = 2

Arithmetic sequence 1, 3, 5, 7……….

3. In the fourth row

Termdifference = 28 – 7 = 21

Position difference = 4 – 1=3

Common difference = 21/3 = 7

Arithmetic sequence 7, 14, 21, 28

4. In the second coloumn 2, –,– 14

Term difference = 14 – 2 = 12

Position difference = 4 – 1=3

Common difference = \(\frac{14-2}{3}=4\)

Arithmetic sequence 2, 6, 10, 14

5. In the third coloumn 3, –, –, 21

Term difference = 21 – 3 = 18

Position difference = 4 – 1=3

Common difference = \(\frac{21-3}{3}=6\)

Arithmetic sequence 3, 9,15, 21

6. In the fourth coloumn 4, –, –, 28

Term difference = 28 – 4 = 24

Position difference = 4 – 1=3

Common difference = \(\frac{28-4}{3}=8\)

Arithmetic sequence 4,12, 20, 28