Question

Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their ${10}^{th}$ terms is the same as the difference between their ${21}^{st}$ terms, which is the same as the difference between any two corresponding terms.
If true then enter $1$ and if false then enter $0$

Answer 1

Let $a,d$ and $a_n$ be the first term, common difference and $n^{th}$ term 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 $A=7$

Also, given that, $a_{10}-A_{10}=a+9d-(A+9d)=a-A=2-7=-5$

and $a_{21}-A_{21}=a+20d-(A+20d)=a-A=2-7=-5$

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

$\therefore$ given statement is true so answer is 1.