Question

Find the common difference of the A.P. and write the next two terms:

(iii) $1.8,2.0,2.2,2.4,...$

Answer 1

Step 1. Note the given data:

Given A.P. is $1.8,2.0,2.2,2.4,...$

First term $t_1=1.8$

Second term $t_2=2.0$

Third term $t_3=2.2$

Fourth term $t_4=2.4$

Let $a$ be the first term of the A.P. and $d$ is the common difference of the A.P.

We need to find the common difference and the next two terms of A.P.

Step 2. Finding the common difference of given A.P:

Formula, the common difference of A.P.$={(n+1)}^{th}term-n^{th}term$

From the Arithmetic Progression, we get

Common difference($d$) $=secondtermofA.P.-firsttermofA.P.$

$$\begin{gathered} =2.0-1.8 \\ =0.2 \end{gathered}$$

Similarly,

$d=t_3-t_2=t_4-t_3=0.2$

Step 3. Finding the fifth term of A.P:

The $n^{th}$term of the AP is $t_n=a+\left(n-1\right)d$.

Here, $a=1.8$, $n=5$, and $d=0.2$.

The fifth term of A.P. $=a+4d$,

$$\begin{gathered} =1.8+4\times (0.2) \\ =1.8+0.8 \\ =2.6 \end{gathered}$$

Step 4. Finding the sixth term of A.P:

The $n^{th}$term of the AP is $t_n=a+\left(n-1\right)d$.

Here, $a=1.8$, $n=6$, and $d=0.2$.

The sixth term of A.P. $=a+5d$

$$\begin{gathered} =1.8+5\times (0.2) \\ =1.8+1.0 \\ =2.8 \end{gathered}$$

So, the common difference of the given A.P. is $0.2$ and next required terms of A.P. are $2.6,2.8$