22) Two APs have the same common difference. The firstterm of one AP is 2 and that of the other is 7. Thedifference between their 10" terms is the same adifference between their 21 terms, which is same asdifference between any two corresponding terms. Why?the

22) Two APs have the same common difference. The firstterm of one AP i

1.	22) Two APs have the same common difference. The firstterm of one AP is 2 and that of the other is 7. Thedifference between their 10" terms is the same adifference between their 21 terms, which is same asdifference between any two corresponding terms. Why?the
Answer» Let the same common difference of two AP’s isd, Given that, the first term of first AP and second AP are 2 and 7 respectively, then the AP’s are2,2 + d,2 + 2d,2 + 3d,.,.and7,7+ d, 7 +2d, 7+3d,…Now, 10th terms of first and second AP’s are 2 + 9d and 7 + 9 d, respectively.So, their difference is 7 + 9d – (2 + 9d) = 5Also, 21st terms of first and second AP’s are 2 + 20d and 7 + 20d, respectively.So, their difference is 7 + 20d – (2 + 9d) = 5Also, if the a„ and bnare the nth terms of first and second AP.Then, bn-an= [7 + (n-1)d)] – [2 + (n-1)d] = 5Hence, the difference between any two corresponding terms of such AP’s is the same as the difference between their first terms.