Answer
(a) Geometric
(b) Not geometric
(c) Not geometric
(d) Geometric
Work Step by Step
(a) Given $$\sum_{n=0}^{\infty} \frac{7^{n}}{29^{n}}$$
This is a geometric series for $c=1$ and $r=\frac{7}{29}$
(b) Given $$\sum_{n=3}^{\infty} \frac{1}{n^{4}}$$
This is not a geometric series because here we can not find the common ratio.
(c) Given $$\sum_{n=0}^{\infty} \frac{n^{2}}{2^{n}}$$
This is not a geometric series because have we can not find the common ratio.
(d) Given$$\sum_{n=5} \pi^{-n}$$
The given series can be written as
$$\sum_{n=5}^{\infty} \frac{1}{\pi^{n}}=\frac{1}{\pi^{5}}+\frac{1}{\pi^{6}}+\frac{1}{\pi^{7}}+\ldots . .$$
Which is a geometric series with $C=\frac{1}{\pi^{5}}$ and $r=\frac{1}{\pi}$
