Question

Find out the arithmetic progression formed when $8$ is added to each term of the arithmetic progression $13,16,19,22,...$ Also find out the arithmetic progression when each term of the above A.P. is subtracted by $8$. Comment on the common difference of the new A.P.

Answer 1

The given arithmetic progression is $13,16,19,22,...$ When $8$ is added to each term of the above arithmetic progression, a new sequence is formed as $21,24,27,29,...$ Thus the new sequence is also an A.P. with the common difference again as $3$. When $8$ is subtracted from the A.P. $13,16,19,22,...$ we have the new A.P. as $5,8,11,14,...$ with the common difference as $3$ again. Thus the common difference remains unchanged even though each term of the A.P. gets added or subtracted by a fixed number such as $8$ as this case.