Question

Find the $8^{\mathrm{th}}$ term from the end of the AP: $7,10,13,...,184$.

Answer 1

Evaluate the required term from the given Arithmetic Progression

Given, AP $=7,10,13,...,184$

As we need to calculate the term from the end, so reverse the AP.

The new AP series will be $184,181,...,13,10,7$

Here, $a=184,d=-3$ and we need to calculate the $8^{\mathrm{th}}$ term

We know that ${\text{n}}^{\mathrm{th}}$ term is $a_n=a+(n-1)d$

Using this formula, we get

$$\begin{gathered} \Rightarrow a_8=184+(8-1)(-3) \\ \Rightarrow a_8=184-21 \\ \Rightarrow a_8=163 \end{gathered}$$

Therefore, the $8^{\mathrm{th}}$ term from the end is $163$.