smileycellist2

2020-11-30

Detemine whether the given sequence geometric or neither if the sequence is srithmetic, find the common difference, if it is geometric, find the common ratio.

If the sequence is arithmetic or geometric, find the$\sum \text{}\text{of}\text{}\left\{{\left(\frac{5}{8}\right)}^{n}\right\}$

If the sequence is arithmetic or geometric, find the

faldduE

Skilled2020-12-01Added 109 answers

Step 1

The given sequence is exponential, it has n in the exponent. So this is a geometric sequence.

Common ratio of the sequence is:

$\frac{second\text{}term}{first\text{}term}=\frac{{\left(\frac{5}{8}\right)}^{2}}{{\left(\frac{5}{8}\right)}^{1}}=\frac{5}{8}$

Step 2

We will use the$\sum $ formula of the geometric series.

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

${S}_{50}=\frac{\frac{5}{8}(1\text{}-\text{}{\left(\frac{5}{8}\right)}^{50})}{1\text{}-\text{}\frac{5}{8}}$

${S}_{50}=\text{}\frac{\frac{5}{8}\text{}(0.999999999938)}{\frac{3}{8}},\text{}{S}_{50}=\text{}\frac{5(0.999999999938)}{3}$

${S}_{50}=1.667$

Answer: Geometric,$\text{common ratio}=\frac{5}{8},\text{}\sum =1.667$

The given sequence is exponential, it has n in the exponent. So this is a geometric sequence.

Common ratio of the sequence is:

Step 2

We will use the

Answer: Geometric,

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