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{of} left{left(frac{5}{8}right)^{n}right}

smileycellist2

smileycellist2

Answered question

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  of {(58)n}

Answer & Explanation

faldduE

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:
second termfirst term=(58)2(58)1=58
Step 2
We will use the formula of the geometric series.
Sn=a1(1  rn)1  r
S50=58(1  (58)50)1  58
S50= 58 (0.999999999938)38, S50= 5(0.999999999938)3
S50=1.667
Answer: Geometric, common ratio=58, =1.667

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