5. What is the value of the first term for each goomotric sorios describod? Express your answers to the nearest tenth, if necessary.
a) $S_{n}=33, I_{n}=48, r=-2$
b) $S_{n}=443, n=6, r=\frac{1}{3}$

Step 1 ：Given the sum of the series (S_n), the number of terms (n), and the common ratio (r), we can use the formula for the sum of a geometric series to find the first term (a): \(S_n = \frac{a(r^n - 1)}{r - 1}\)

Step 2 ：Rearrange this formula to solve for a: \(a = \frac{S_n (r - 1)}{r^n - 1}\)

Step 3 ：For the first series (a), plug in the given values: \(S_n = 33, n = 48, r = -2\)

Step 4 ：Calculate the first term for series (a): \(a = \frac{33(-2 - 1)}{-2^{48} - 1}\)

Step 5 ：Approximate the first term for series (a) to the nearest tenth: \(a \approx 0\)

Step 6 ：For the second series (b), plug in the given values: \(S_n = 443, n = 6, r = \frac{1}{3}\)

Step 7 ：Calculate the first term for series (b): \(a = \frac{443(\frac{1}{3} - 1)}{(\frac{1}{3})^6 - 1}\)

Step 8 ：Approximate the first term for series (b) to the nearest tenth: \(a \approx 295.7\)

Step 9 ：\(\boxed{\text{Final Answer:}}\) a) The first term for the geometric series is approximately 0 (to the nearest tenth). b) The first term for the geometric series is approximately 295.7 (to the nearest tenth).