Question

Which term of the A.P. $3,8,13,18,...$ is $78$?

Answer 1

Determine which term of the A.P. $3,8,13,18,...$ is $78$.

From the given data. first term is $a=3$, common difference is $d=8-3=5$ and $a_n=78$.

Apply the $n^{\mathrm{th}}$ term formula: $a_n=a+\left(n-1\right)d$

Calculate the value of $n$.

$$\begin{gathered} a_n=a+\left(n-1\right)d \\ \Rightarrow 78=3+\left(n-1\right)5 \\ \Rightarrow 78=3+5n-5 \\ \Rightarrow 78=-2+5n \\ \Rightarrow 5n=80 \\ \Rightarrow n=\frac{80}{5} \\ \therefore n=16 \end{gathered}$$

Hence, the ${16}^{\mathrm{th}}$ term of the given A.P. is $78$.