Question

Find out the arithmetic progression formed when $4$ is multiplied to each term of the arithmetic progression $8,6,4,2,...$ Also find out the arithmetic progression when each term of the above A.P. is divided by $4$. Comment on the common difference of the new A.P.

Answer 1

The given arithmetic progression is $8,6,4,2,...$ When $4$ is multiplied to each term of the above arithmetic progression, a new sequence is formed as $32,24,16,8,...$ Thus the new sequence is also an A.P. with the common difference now as $8$. Or, in other words we can say that the new common difference is $4$ times the previous common difference. When each term of the A.P. $8,6,4,2,...$ is divided by $4$ we have the new A.P. as $2,1.5,1,0.5,...$ with the common difference now as $0.5$ of the new A.P. Thus the common difference of the previous A.P. gets divided by $4$ too.