54. Two A.Ps have the same common difference. The first term of one A.

1.	54. Two A.Ps have the same common difference. The first term of one A.P. is 2 and thatoother is 7. The difference between their 10th terms is the same as the difference betinetheir 21t terms, which is the same as the difference between any twoterms. Why?INCERT EXEMPLA
Answer» Let us assume difference in consecutive terms in first AP = x difference in consecutive terms in second AP = y. 10th term in both APs are 2+(10-1)x and 7+(10-1)y i.e. 2+9x and 7+9y. 21st terms in both APs are 2+20x and 7+20y. Since the differences of consecutive terms are same, 7+9y-(2+9x) = 7+20y-(2+20x) 9(y-x) = 20(y-x) That means y-x = 0. Implies y = x. The difference between consecutive terms in both APs is same.

54. Two A.Ps have the same common difference. The first term of one A.P. is 2 and thatoother is 7. The difference between their 10th terms is the same as the difference betinetheir 21t terms, which is the same as the difference between any twoterms. Why?INCERT EXEMPLA

Answer»

Let us assume difference in consecutive terms in first AP = x

difference in consecutive terms in second AP = y.

10th term in both APs are 2+(10-1)x and 7+(10-1)y

i.e. 2+9x and 7+9y.

21st terms in both APs are 2+20x and 7+20y.

Since the differences of consecutive terms are same,

7+9y-(2+9x) = 7+20y-(2+20x)

9(y-x) = 20(y-x)

That means y-x = 0.

Implies y = x.

The difference between consecutive terms in both APs is same.