Question

Two A.P.'s have the same common difference. The first term of one of these is $3$, and that of the other $8$. What is the difference between their $2^{nd}$ term.

Answer 1

Solution:-

Let the two A.P.'s be $A_1,A_2,A_3,.............,A_n$ and $a_1,a_2,a_3,............,a_n$.

Let the common difference of two A.P.'s be 'd'.

Given that first term of one of these is 3, and that of the other 8.

Let $A=8\&a=3$

As we know that,

$a_n=a+(n-1)d$

$\therefore A_2-a_2=A+d-(a+d)$

$\Rightarrow A_2-a_2=A+d-a-d=A-a=8-3=5$

Hence, the correct answer is $5$.