Question

Select the following series as arithmetic, geometric, or neither. 3/2 + 3/4 + 3/8 + 3/16 + 3/32

Answer 1

Answer:

Geometric

Step-by-step explanation:

Given : $\frac{3}{2} +\frac{3}{4} +\frac{3}{8}+\frac{3}{16} + \frac{3}{32}$

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.

$d=a_2-a_1=\frac{3}{4}-\frac{3}{2}=\frac{3-6}{4}=\frac{-3}{4}$

$d=a_3-a_3=\frac{3}{8}-\frac{3}{4}=\frac{3-6}{8}=\frac{-3}{8}$

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.

$r =\frac{a_2}{a_1}=\frac{\frac{3}{4}}{\frac{3}{2}}=\frac{2}{4}=\frac{1}{2}$

$r =\frac{a_3}{a_2}=\frac{\frac{3}{8}}{\frac{3}{4}}=\frac{4}{8}=\frac{1}{2}$

Since the ratio between the consecutive terms are same .

So, The given sequence is G.P.