Identify whether the series is an arithmetic series (AS), geometric series (GS) or not one of the difined types ( NASGS ) and determine the sum (for NASGS, write NO SUM). Write your Solution. a. 1+frac32+frac94+...+frac{81}{16}

Aneeka Hunt 2020-11-12 Answered
Identify whether the series is an arithmetic series (AS), geometric series (GS) or not one of the difined types ( NASGS ) and determine the sum (for NASGS, write NO SUM). Write your Solution.
a. 1+32+94+...+8116
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Expert Answer

faldduE
Answered 2020-11-13 Author has 109 answers
Given series is 1+32+94+...+8116
Here, we have
a1=1,a2=32,a3=94
a2a1=(32)1=32
a3a2=(94)(32)=32
We get that a2a1=a3a2.
Sice, the ratio of terms is same.
Therefore, given series is geometric where common ratio is r=32
Now, we know that n-th term of geometric series is given as:
an=a1rn1
8116=(1)(32)n1
(32)4=(32)n1
On comparing both sides, we get
n1=4
n=5
Therefore, number of terms in series is 5.
Sum of geomteric series is given as:
Sn=a1(rn1)r1
Therefore, sum of the given geometric series will be:
S5=1((32)51)321
=24332112
=2113212
=21116
Hence, sum is =21116
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Jeffrey Jordon
Answered 2021-12-27 Author has 2047 answers

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