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 2020-11-30 Answered
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}
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Expert Answer

faldduE
Answered 2020-12-01 Author has 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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