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

## Question

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

## 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 \(158.\)