Question

Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution. a. frac{1}{3}, frac{2}{9}, frac{3}{27}, frac{4}{81}, ... b. 3, 8, 13, 18, ..., 48

Polynomial arithmetic
Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution. a. $$\frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81}, ...$$ b. $$3, 8, 13, 18, ..., 48$$
Step 1 Given the sequence $$(a) \frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81},...$$ Common difference, $$d = t_1 − t_2 = \frac{2}{9} − \frac{1}{3} = \frac{-1}{3} \neq t_4 − t_3= \frac{-5}{81}$$ The sequence (a) is not arithmetic . Common ratio $$r = \frac{t_2}{t_1} = \frac{3}{2} \neq \frac{7}{2} = \frac{t_3}{t_2}$$ The sequence (a) is not geometric. The given sequence is none of the above mentioned types. $$ul O (a)\frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81},...$$ Step 2 $$(b) 3,8,13,18,...48$$ Common difference, $$d = t_1 − t_2 = 8 − 3 = −5 = t_3 − t_2 = 13−8 = −5= t_4 − t_3 = −5= .....$$ The given sequence (b) is arithmetic. $$ul A (b) 3,8,13,18,...48$$