# Ex.5.2 Q6 Arithmetic Progressions Solution - NCERT Maths Class 10

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## Question

Check Whether $$-150$$ is a term of the AP $$\,11,\,8,\,5,\,2\,\dots$$

Video Solution
Arithmetic Progressions
Ex 5.2 | Question 6

## Text Solution

What is Known:?

The AP

What is Unknown?

Whether $$-150$$ is a term of AP.

Reasoning:

$${a_n} = a + \left( {n - 1} \right)d$$

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:

$$11,\,8,\,5,\,2$$ are in AP

First term $$a = 11$$

Common difference $$d = 8--11 = - 3$$

\begin{align}{a_n} &= a + (n - 1)d\\a + (n - 1)d &= - 150\\11 + (n - 1)( - 3) &= - 150\\n - 1 &= \frac{{161}}{3}\\n &= \frac{{164}}{3}\end{align}

$$n = \frac{{164}}{3}$$ which is a fraction. Given number is not a term of AP $$11,\, 8,\, 5,\, 2\,\dots$$$$n$$ should be positive integer and not a fraction.

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