# Ex.5.1 Q3 Arithmetic progressions Solutions - NCERT Maths Class 10

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## Question

For the following APs, write the first term and the common difference:

\begin{align} &\rm{i)}\,\,3,1, - 1, - 3 \ldots \ldots \\ &\rm{ii)}\,\, - 5, - 1,3,7 \ldots \ldots \\ &\rm{iii)}\,\,\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{{13}}{3} \ldots \ldots.\quad \quad \\ &\rm{iv)}\,\,0.6,1.7,2.8,3.9 \ldots \end{align}

Video Solution
Arithmetic Progressions
Ex 5.1 | Question 3

## Text Solution

Reasoning:

General form of an arithmetic progression is \begin{align}{a, (a+d), (a+2d), (a+3d)…}\end{align} where $$a$$ is the first term and $$d$$ is the difference.

i) What is known?

$$3,1,-1,-3$$ are in AP.

What is Unknown?

First term and the common difference of the AP.

Steps:

The AP is \begin{align} 3, 1 ,-1, -3.\end{align}

First term \begin{align}{a = 3}.\end{align}

\begin{align}\text{Common difference} & = {a_2} - {a_1}\\&= 1 – 3\\&= -2\end{align}

First term is $$3$$ and the common difference is $$-2.$$

ii) What is known?

\begin{align}-5, -1, 3, 7\end{align} are in AP

What is Unknown?

First term and the common difference of the AP.

Step:

The AP is \begin{align}-5, -1, 3, 7.\end{align}

First term\begin{align} a = - 5\end{align}

\begin{align} \text{Common difference} & = {a_2} - {a_1}\\&= -1 – (-5)\\&= -1 + 5\\& = 4\end{align}

First term $$-5$$ and the common difference is $$4.$$

iii) What is known?

\begin{align}\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{{13}}{3}\end{align} are in AP.

What is Unknown?

First term and the common difference of the AP.

Steps:

The AP is  \begin{align}\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{{13}}{3}\end{align}

First term \begin{align} a = \frac{1}{3}\end{align}

\begin{align}\text{Common difference} &= {a_2} - {a_1}\\&= \frac{5}{3} - \frac{1}{3}\\&= \frac{{5 - 1}}{3}\\&= \frac{4}{3}\end{align}

First term is \begin{align}\frac{1}{3}\end{align} and the common difference is \begin{align}\frac{4}{3}\end{align}

iv) What is known?

\begin{align}{\rm{0}}{\rm{.6,}}\,\,{\rm{1}}{\rm{.7,}}\,\,{\rm{2}}{\rm{.8,}}\,\,{\rm{3}} {\rm{.9}}\end{align} are in AP.

What is Unknown?

First term and the common difference of the AP.

Steps:

The AP is  \begin{align} {\rm{0}}{\rm{.6,}}\,\,{\rm{1}}{\rm{.7,}}\,\,{\rm{2}}{\rm{.8,}}\,\,{\rm{3}}{\rm{.9}}\end{align}

First term \begin{align} a = 0.6 \end{align}

\begin{align} \text{ Common difference}&= {a_2} - {a_1}\\&= 1.7 – 0.6\\&= 1.1\end{align}

First term $$= 0.6$$ and the common difference $$= 1.1$$

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