Question

Two Ap have the same common difference. The first term ofvan Ap is 2 and that of the other is 7. The difference between their 10th term is the same as the difference between any two corresponding term . Why?

Answer 1

The difference between consecutive terms in both APs is same.

That is the reason, all corresponding terms in both APs have same difference.

Step-by-step explanation:

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.