Answer
a)
\begin{array}{c|ccc}& \textbf{Term} & \textbf{Value} & \textbf{Ones Digit}
\\\hline1 & 7^1 & 7 & 7
\\2 & 7^2 & 49 & 9
\\3 & 7^3 & 343 & 3
\\4 & 7^4 & 2401 & 1
\\5 & 7^5 & 16807 & 7
\\6 & 7^6 & 117649 & 9
\\7 & 7^7 & 823543 & 3
\\8 & 7^8 & 5764801 & 1
\end{array}
b) 9
Work Step by Step
The ones digit sequence repeats every 4th entry.
34 is two past a multiple of 4 (32), so the ones digit at entry 34 is the same as the ones digit at entries 2 and 6. The ones digit at entry 34 is 9.
