Question

Find the ${20}^{\mathrm{th}}$ term from the last term of the AP: $3,8,13...,253$

Answer 1

Evaluate the required term from the given Arithmetic Progression

Given, $AP=3,8,13...,253$

As we need to evaluate the ${20}^{\mathrm{th}}$ term from last, we will put the AP in reverse order, i.e. $253,248,....,13,8,3$

Here, first term $a=253$,

and, common difference $d=248-253=-5$

We know that ${\mathrm{n}}^{\mathrm{th}}$ term of an AP is defined by $a_n=a+(n-1)d$

So, to evaluate the ${20}^{\mathrm{th}}$ term, we will calculate $a_{20}$

$$\begin{gathered} \Rightarrow a_{20}=253+(20-1)(-5) \\ \Rightarrow a_{20}=253-95 \\ \Rightarrow a_{20}=158 \end{gathered}$$

Hence, the ${20}^{\mathrm{th}}$ term from last will be $158$.