Question

Find the common difference of the A.P. and write the next two terms:$75,67,59,51,...$

Answer 1

Step 1. Find the common difference.

We,have

First Term $a_1=75$

Second Term $a_2=67$

Third Term $a_3=59$

Fourth Term $a_4=51$

Common difference of A.P. is given by

$d=a_n-a_{n-1}$

Now putting $n=2$

$$\begin{gathered} d=a_2-a_1 \\ =67-75 \\ =-8 \end{gathered}$$

Therefore, the Common difference$\left(d\right)$ of A.P. is $-8$

Step 2. Find the next two term.

We know, the nth term of an A.P. is given by

$a_n=a_1+(n-1)d$

We have to find fifth and the sixth term

$$\begin{gathered} a_1=75 \\ d=-8 \end{gathered}$$

$$\begin{gathered} a_5=a_1+(5-1)d \\ =75+4(-8) \\ =75-32 \\ =43 \\ {a}_6=a_1+(6-1)d \\ =75-40 \\ =75+5(-8) \\ =35 \end{gathered}$$

Therefore, the next two term are $43$ and $35$.

Hence, the common difference of the A.P is $-8$ and the next two term are $43$ and $35$.