Question

two APs have same common difference. the first term of one AP is 2 and that of the other is 7. the difference between their tenth terms is the same as the difference between their twentyfirst terms, which is same as the difference any two corresponding terms. why??????

Answer 1

Answer:

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.

Answer 2

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 are

2,2 + d,2 + 2d,2 + 3d,.,.

and  7,7+ 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) = 5

Also, 21st terms of first and second AP’s are 2 + 20d and 7 + 20d, respectively.

So, their difference is 7 + 20d – (2 + 9d) = 5

Also, if the a„ and bn are the nth terms of first and second AP.

Then, bn -an = [7 + (n-1)d)] – [2 + (n-1)d] = 5

Hence, the difference between any two corresponding terms of such AP’s is the same as the difference between their first terms.

Hope it will help you out