The first term of a geometric sequence is 8, the second term is 24, & the 3rd term is 72.  What is the sum of the first 12 terms of the corresponding series?

Q: alculate the next term in the geometric sequence that is calculated with a ratio of 24 if the…

A: Definition used -                   Geometric sequence -                          It is a sequence…

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 1, 5, 5,…

A: G. P. Series problem.....

Q: The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find…

A: The first term of the arithmetic sequence, a1 =6 he common difference,d= 3

Q: The first term of a geometric sequence is 4, and the second term is 1. Find the 5th term

A: given that ,in geometric sequence  first term=4 second term=1 find the 5th term? for geometric…

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: Find the sum, if it exists, of the infinite geometric series related to 64(1) . n-1 the infinite…

A: So option (b) is correct.using the formula  S=a/1-r

Q: The first term of a geometric sequence is 8 and the fourth term is 216. What is the sum of the first…

A: Given: In a Geometric series (GS), First term a1=a=8 Fourth term a4=216 To find: Sum of first 12…

Q: What is the difference between an infinite sequence and an infinite series?

A: Solution: Infinite Sequence: An infinite sequence of numbers is an ordered list of numbers with an…

Q: For a given geometric sequence, the  4th  term,  a4 , is equal to  −3127 , and the  8th  term,…

A: To find: The value of tenth term a10 Given information: a4=-3127, a8=-93 Concept used: The general…

Q: If the 8th term of an arithmetic series 39 and the 20th term is -33. What is the common difference?

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Q: The third term of the arithmetic sequence is 72 and the number of the third term with the fifth term…

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Q: If the 100th term of an arithmetic sequence is 584, and its common difference is 6, then its first…

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Q: In a certain geometric sequence, the eighth term is 100 and the common ratio is -(3/2). Find the…

A: Let the first term be a so the sequence will be a, ar, ar2, ar3 ....... The eighth term is 100…

Q: The first term of a geometric sequence is  1536 and the common ratio is 1 /2 . Which term of the…

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Q: A geometric sequence has a first term of 8/3 (fraction) and a fourth term of 9.  Find the common…

A: For the given GPfirst term a=83fourth term T4=9 To find the common ratio r

Q: When finding the nth term in an arithmetic sequence, how do I sole a sequence with fractions? For…

A: In order to find the nth term in an arithmetic sequence of fractions, one should be able to find the…

Q: *30. Formulate Substitute the formula for the nth term of an arithmetic sequence (105) into the…

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Q: The sum of the first n terms of a sequence is (17n^2 )– 11n. Determine the 20th term.

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Q: The first term of a geometric sequence is 8 and the fourth term is 216. What is the sum of the first…

A: Given, First term = 8 Fourth term = 216

Q: The first term of a geometric sequence is 8, the second term is 24, & the 3rd term is 72. What is…

A: We have to find the sum of the first 12 terms of the geometric sequence where first term is 8,…

Q: 3 What is the sum of the geometric series

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Q: If the common difference of an Arithmetic series is 6 and the 4th term is 10, what is the value of…

A: Sol

Q: If the general term of an arithmetic sequence is a(n) = 7n - 3, find the sum of the first 7 terms of…

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Q: 4. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?…

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Q: Find the sum, if it exist, of the infinite geometric series related to the infinite geometric…

A: we have to find the sum of the given geometric series

Q: The first term of an arithmetic sequence is 10, and the tenth term is 2.(a) Find the common…

A: a = 10 ,   a10 = 2   Using an = a + n - 1da a10 = a +  n - 1 d         2  = 10 + 9 d2 - 10  = 9d…

Q: 3. The 3rd term of a geometric sequence is 12 and the 7th term is 192. Determine the 13th term.

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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: 3a. The first term of a geometric sequence is 36 and the fourth term is 1/6. What is the value of r?…

A: We have to find r

Q: The median of the first five terms of a geometric sequence is 4. The ratio of the first term to the…

A: Let the terms of the GP be a,ar,ar^2,ar^3..

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: The first term of a geometric sequence is 12, and the third term is 16/3. Find the fifth term.…

A: Given that first term of the geometric sequence is 12. Third term of the third term is 16/3. We have…

Q: Find the sum of the first five terms of the sequence with the given general term. an = (−1)n

A: Given sequence, an=(-1)n Put n=1 to 5 to get first five terms of sequence then add them.

Q: The sixth term of an arithmetic sequence is 28 and the ninth term is 36. Count the sum of the first…

A: We use the sum of an arithmetic sequence to answer the given question.

Q: The 13th term of a sequence is 8, and the 17th term is 8. What is th

A: Given, the 13th term of a sequence is 8 and 17th term of sequence is 8.

Q: What is the difference between a geometric sequence and an infinite geometric series?

A: Given: Geometric sequence and an infinite geometric series

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

A:

Q: what would the sum be of the first 10 numbers in that series

A: Let's find sum of the series.

Q: Given that the first term of an arithmetic sequence is 50 and the common difference is -5, what is…

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Q: For a given geometric sequence, the 1st term, a₁, is equal to 11 9 your answer as a fraction. and…

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Q: The fifth term of an arithmetic sequence is 24, and the sum of the first 10 terms is 265. Write the…

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Q: Given a geometric sequence whose first term is 3 and its common ratio is Find i) the 8 term, ii) the…

A: a=3  &  r=12. i. Eighth term is, T8=ar7    ∵Tn=arn-1=3127=3128

Q: The sum of the first five terms of the arithmetic sequence is -5 and the sixth term is -10. The sum…

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Q: If the 100th term of an arithmetic sequence is 213, and it's common difference 2, then what is the…

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Q: The 7th term of an arithmetic sequence is −44, and the common difference is −4. Find the first term.

A: The nth term of sequence is given by:…

Q: For a given geometric sequence, the  8th  term,  a8 , is equal to  239 , and the  11th  term,…

A: The nth term of the G.P series is given by an=arn-1 where a is the first term and r is the common…

Q: The first term a, of a geometric sequence is 10 and the common ratio r is 5, find the sum of first…

A:

Q: The fourth term of a geometric sequence is 135 3645 and the seventh term is 4. Find the first 32…

A: Given :                     The fourth term of the geometric sequence is 1354 and seventhterm of…

Q: What are the first three terms of the sequence given that the nth-term formula is an=n/(n+1).

A: Given, nth-term of sequence is an=nn+1  find first three terms of the sequence-

Q: certain bacteria triples in amount everyday. If there are 100 bacteria presemt during day 1, what…

A: To calculate total count of bacteria after 10 days.

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.