If 1 + 5 + 9 + …..x = 780 then x is

$$\begin{gathered} 1+5+9+ +x=780 \\ \Rightarrow sum of n terms in A.P=\frac{n}{2}\left(2a+\left(n-1\right)d\right)=780 \\ \Rightarrow \frac{n}{2}\left(2\left(1\right)+\left(n-1\right)4\right)=780 \\ \Rightarrow n\left(2n-1\right)=780 \\ \Rightarrow 2n^2-n-780=0 \\ \Rightarrow n=20 \end{gathered}$$
$now x= nth term =a+\left(n-1\right)d=1+\left(19\right)\left(4\right)=77$