A series has four terms, starts with $5$, and has a sum of $200$.

1. What are the terms if the series is arithmetic?

   Hint (a):

   Step 1(a):

   Step 2(a):

   Step 3(a):

   Step 4(a):

   Step 5(a):

   $S=\frac{n(a_{1}+a_{n})}{2}$

   $200=\frac{4(5+a_{n})}{2}$

   $400 = 20 + 40a_{n}$

   $380 = 40a_{n}$

   $95 = a_{n}$

   $\frac{95-5}{3}=30$

   Answer (a):

   Series $= 5 + 35 + 65 + 95$

2. What are the terms if the series is geometric?

   Hint (b):

   Step 1(b):

   Step 2(b):

   Step 3(b):

   Step 4(b):

   $S=\frac{a(r^{n}-1)}{r-1}$

   $200=\frac{5(r^{4}-1)}{r-1}$

   $200=\frac{5(r-1)(r+1)(r^{2}+1)}{r-1}$

   $200 = 5\left(r + 1\right)\left(r^{2} + 1\right)$

   By inspection $= 3$.

   Answer (b):

   Series $= 5 + 15 + 45 + 135$