Find the sum, if it exists, of the infinite geometric series related to the infinite geometric sequence described by a(^n)=12(0.2)^n-1

Q: If third and seven terms of geometric sequence is 45 and 100 respectively.then find its nineteenth…

A: Given data: The third term is a3=45. The seventh term is a7=100.

Q: The sum of the first n terms of a geometric sequence is 341. If aj = and a4 , what is the value of…

A: 1. Geometric progression (GP) is a type of sequence where each succeeding term is produced by…

Q: Find the nth term of a sequence whose first several terms are given. 4, -16, 64, –256, . . an

A: Given that: Sequence: 4, -16, 64, -256, ...

Q: The sum of an infinite geometric series is 108, while the sum of the first 3 terms is 112. Determine…

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Q: what is the 20th term in a geometric series whose 5th term is 48 and 12th term is 6144? Please show…

A: In a geometric series nth term an=arn-1  where a = first term             r = common ratio  Given…

Q: Find the sum of the first EIGHTEEN terms of the given sequence where - is the eighteenth term. *If…

A: Topic:- sequence and series

Q: Find the 5th term of the geometric sequence with first terma1 = 5 and common ratio r = - 2

A: A geometric sequence is a sequence where each term is found by multiplying the previous term by a…

Q: , find the sum of the infinite geometric series.

A:

Q: What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64?

A: Here we have to find the common ratio of the geometric sequence whose first term is 27 and fourth…

Q: Find the sum of 150 terms if the series is 6,(9/2), 3,....

A: Determine the common difference of the series. d=92-6=-1.5 Determine the sum of the series using the…

Q: Find the 30th partial sum of the arithmetic sequence:   78, 76, 74, 72,\70, ....

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Q: Find the Sum of the Series 는 - 논(는,늘(는)` - 음은)

A:

Q: Find the sum of the infinite geometric series if it exists.

A: 2+23+29+227+---- It is an infinite geometric series with, First term=a=2Common ratio=r=232=13

Q: Find the sum of the first eight terms of the sequence 1/8,−1/4 ,1/2 ,.... please show working

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Q: What is the sum of the first 10 terms of the sequence {300, 150, 75, ...}?

A: Given: 300,150,75,...... Formula Used: Sn=a1-rn1-r

Q: Find the first four terms and the seventh term of the sequence that has the given nth term.

A: To find first four terms and seventh term of sequence .

Q: Find the sum of the first 27 terms of the arithmetic sequence. 19, 28, 37, 46, .. What is the sum of…

A: Topic = Sequence

Q: Find the first term and the common difference of the arithmetic sequence whose 9th term is – 28 and…

A: To find: The first term and common difference of the arithmetic sequence. Given: The 9th term of the…

Q: Find the sum of the first 28 terms of the arithmetic sequence. 36, 44, 52, 60, .. What is the sum of…

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Q: Find the 38th term of a sequence where the first term is −11 and the common difference is 2.

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Q: Find the first term and the common difference of the arithmetic sequence whose 6th term is – 9 and…

A: Explanation of the solution is given below...

Q: Find the sum, exists of the infinite geometric series that is related to the infinite geometric…

A: To find the sum

Q: The geometric mean between the first two terms in a geometric sequence is 32. If the third term is…

A:

Q: In your own words, describe how a function defined by a power series behaves like a polynomial.

A: Power series of the form ∑n=1∞anxn and a polynomial is of the form ∑n=1kanxn

Q: The sum of the first four terms of a geometric series is 100.8352 and the common ratio is 0.6. Write…

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Q: Find the sum, if it exists, of the infinite geometric series that is related to the infinite…

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Q: Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said…

A: Given:  The 1 infected person infects 33 other persons in the worst case scenario.    To find:  The…

Q: Find the sum of the first 15 terms for the sequence: 7,10, 13, 16, 19,

A: We have 7,10,13,16,19,.........15th termFirst term a=7common Difference d=10-7=3

Q: Find the sum of the first 14 terms of the geometric sequence: , 3, -6, 12, ...

A: Given geometric sequence is,

Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, . . . an

A: We have to find nth term

Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, ... an =

A:

Q: Find the sum of the finite geometric sequence whose first term is 1.6, whose ratio is 0.5, and which…

A: Gp

Q: To at least 3 significant figures, find the sum of the first 45 terms of this geometric sequence: -…

A: The given problem is to find the sum of first 45 terms of the given geometric sequence,  Given…

Q: Find the 16th term of an arithmetic sequence if the first term is 26 and the common difference is .…

A:

Q: The bob of a pendulum swings through an arc 24 centimeters long on its first swing. If each…

A: G.P SeriesA series, in which each term is found by multiplying by the previous term by a fixed term.…

Q: Calculate the sum of the first 38 terms in the sequence. 7, 3, - 1, – 5, ... | The sum is

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Q: Find the 100th arithmetic sequence with 1st term 5 and eighth term 19

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Q: Find the 25th partial sum of the arithmetic sequence 75, 70, 65, 60,...,

A: Let's find.

Q: Find the sum of the infinite geometric series if it exists.

A: To find: The sum of given infinite geometric series. Given information: The series is 1-12+14-18+⋯…

Q: Find the sum of the first 20 terms of the sequence 5, 10, 15, 20, ...

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Q: If the sum of second and tenth terms of arithmetic sequence is equal to 12, find sum of fourth,…

A: A sequence (an) is said to be arithmetic is a2-a1=a3-a2=a4-a3=...=d(say)That is, d=an-an-1 for…

Q: Find the sum of the first 50 terms of the sequence: -2, 0, 2, 4, . . . .

A: -2, 0, 2, 4, ...... It is an arithmetic sequence with, First term=a=-2Common difference=d=2

Q: Find the sum of the first 11 terms of the geometric sequence: 7, -21, 63, -189, 567, . . . .

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Q: Find the sum of the first 12 terms of the geometric sequence whose first term is 11 and whose common…

A: Given a geometric series with first term 11 and common ratio 5.

Q: Find the first term and the common difference of the arithmetic sequence whose 9th term is – 17 and…

A: The general form of arithmetic sequence is a,a+d,a+2d,......,Where a  is the first term of the…

Q: Find the nth term of a sequence whose first several terms are given. 7, 2, –3, –8, ... an

A:

Q: Find the sum of the first 100 terms of an arithmetic sequence with 15th term of 90 and first term of…

A: 15th term is 90 and the first term is 6 of an arithmetic sequence. To find the sum of its first 100…

Q: Find the sum of the first 8 terms of the sequence. Show all work for full credit. 1, -3, -7, -11,…

A: It is ap.  Use formula of sum of n term of ap.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.