Respuesta :
Answer:
Geometric
Step-by-step explanation:
Given : [tex]\frac{3}{2} +\frac{3}{4} +\frac{3}{8}+\frac{3}{16} + \frac{3}{32}[/tex]
To Find: the following series as arithmetic, geometric, or neither.
Solution:
Find the common difference d .
If difference between the consecutive terms are same . So, the series is arithmetic.
[tex]d=a_2-a_1=\frac{3}{4}-\frac{3}{2}=\frac{3-6}{4}=\frac{-3}{4}[/tex]
[tex]d=a_3-a_3=\frac{3}{8}-\frac{3}{4}=\frac{3-6}{8}=\frac{-3}{8}[/tex]
Since the common difference is not same between the two consecutive terms . So, The given series is not arithmetic.
Now find the common ratio r
If the ratio between the two consecutive terms are same than the sequence is geometric.
[tex]r =\frac{a_2}{a_1}=\frac{\frac{3}{4}}{\frac{3}{2}}=\frac{2}{4}=\frac{1}{2}[/tex]
[tex]r =\frac{a_3}{a_2}=\frac{\frac{3}{8}}{\frac{3}{4}}=\frac{4}{8}=\frac{1}{2}[/tex]
Since the ratio between the consecutive terms are same .
So, The given sequence is G.P.
