# Ex.5.2 Q17 Arithmetic Progressions Solution - NCERT Maths Class 10

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## Question

Find the $$20^\rm{th}$$ term from the last term of the A.P. $$3, \,8,\, 13,\, \dots 253$$

Video Solution
Arithmetic Progressions
Ex 5.2 | Question 17

## Text Solution

What is Known:?

The AP

What is Unknown?

$$20^\rm{th}$$ term from the last term of AP.

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:

Given A.P. is $$3,\, 8,\, 13,\, \dots,253$$

From Given,

As the $$20^\rm{th}$$ term is considered from last $$a = 253$$

Common difference, $$d = 3 - 8 = - 5$$ (Considered in reverse order)

We know that the $$n\rm{th}$$ term of an A.P. Series,

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

Hence $$20^\rm{th}$$ Term, $${a_{20}} = a + (20 - 1)d$$

\begin{align}{a_{20}} &= 253 + (20 - 1)( - 5)\\& = 253 - 19 \times 5\\ &= 253 - 95\\& = 158\end{align}

Therefore, $$20^\rm{th}$$ term from the last term is $$158.$$