Question

Tavo Two AP's have the same common difference The first
term of one AP is 2 and that of other 7. The differe
between their loth term is same as difference between
ony two coresponding terms why?​

Answer 1

Step-by-step explanation:

Let a,d and a

n

be the first term, common difference and n^{th} of first AP and A,d and A

n

be the first term, common difference and n^{th} term of second AP respectively.

Given a=2 and A=7 a

10

−A

10

=a+9d−(A+9d)=a−A=2−7=−5

Difference between any two corresponding terms of these AP's is equal to difference between first terms of these AP's.

⇒ given statement is true so answer is 1.

Answer 2

Correct question :

Two AP's have the same common difference. The first term of one AP is 2 and that of the other is 7. the difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms? Why?

Solution :

Let the same common difference of two AP 's is d.

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 + 9d, 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 b, are the nth tems of first and second AP.

Then,

b_n - a_n = [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.