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# Ex.5.2 Q9 Arithmetic Progressions Solution - NCERT Maths Class 10

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## Question

If the $$3^\rm{rd}$$ and the $$9^\rm{th}$$ terms of an AP are $$4$$ and $$-8,$$ respectively, which term of this AP is zero.

Video Solution
Arithmetic Progressions
Ex 5.2 | Question 9

## Text Solution

What is Known:?

$$3^\rm{rd}$$ and $$9^\rm{th}$$ term of AP,

What is Unknown?

Which term of AP is zero.

Reasoning:

$${a_n} = a + \left( {n - 1} \right)d$$ is the general term of AP. Where $${a_n}$$ is the $$n\rm{th}$$ term, $$a$$ is the first term, $$d$$ is the common difference and $$n$$ is the number of terms.

Steps:

Third term of the AP $$= 4$$

$a + 2d = 4 \qquad \dots\left( 1 \right)$

$$9^\rm{th}$$ term of AP $$= -8$$

$a + 8d = - 8 \qquad \ldots .\left( 2 \right)$

Solving (1) and (2) for $$a$$ and $$d$$

\begin{align}& \frac{\begin{align}& a\text{ }+\text{ }2d\text{ }=4 \\ & a\text{ }+\text{ }8d\text{ }=-8 \\ \end{align}}{-6d\text{ }=\text{ }12} \\ &\qquad \; d\text{ } =-2 \\\end{align}

Putting $$d = - 2$$ in equation (1)

\begin{align}a - 4 = 4\\a = 8\end{align}

\begin{align}a + (n - 1)d &= 0\\8 + (n - 1)( - 2)& = 0\\n - 1 &= 4\\n &= 5\end{align}

$$5^\rm{th}$$ term will be $$0.$$

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