consider the sequence (a^n)n≥0 which starts 3,14,25,36,.... a. what is the next term in the sequence ? find a formula for the Nth term of this sequence. a^n= _________

Q: Find the sum of the first 90 terms of the geometric sequence. Show your work with the formulas 4800,…

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Q: Construct a difference table to predict the next term of the sequence. −1, 4, 23, 60, 119, 204,…

A: To construct a difference table to predict the next term of the sequence. −1, 4, 23, 60, 119, 204,…

Q: create a sequence with five terms based on the given information.  An arithmetic sequence with a…

A: Given that the third term of the arithmetic sequence is 8 and the common difference is 5.That is a3…

Q: Find the 7th term in this sequence:2.5,7.5,22.5,67.5...

A: The sequence is2.5 , 7.5 , 22.5 , 67.5 which is in geometric progressionwith a =2.5 , r = 7.52.5 = 3

Q: There is a job that starts at $30,000 per year. Each year the salary increases by 4%. Find out the…

A: Given:There is a job that starts at $30,000 per year. Each year the salary increases by 4%.

Q: What is the 100th term of the sequence –3, 2, 7, 12, ...?

A: Given: Sequence: –3, 2, 7, 12, ...?   To find: 100th term of the sequence. Formula to be used:…

Q: Determine the first six terms of the sequence defined by t₁ = -5 and t = -3t-1 + 8. -5, 23, -61,…

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Q: The second and fifth terms in an arithmetic sequence are 12 and 18 respectively. What is the 100th…

A: Use  an=a1+n-1d  to solve the problem.

Q: What is the eighth term of the arithmetic sequence? 8 -7 -6 -5 tn +4 -3 -2 -2 -3 4 -6 -7 -8

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Q: Find the sum of the first 845 terms of the sequence shown: 22, 18, 28, 37, 34, 56, 40, 75, ... sum =

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Q: What is the formula for the nth term of the sequence 5, 8, 11, 14, ...?

A: The given sequence 5, 8, 11, 14,........

Q: Find the sum of the first 94 terms of the arithmetic sequence   11,15,19,23,27, . . . .

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Q: 2. Find the nth term of the sequences below: а. 3, -5, 7,- 9, 11, b. О, 2, 6, 12, 20, . с. 99, 199,…

A: Topic:- series  Note:- as per our guideline if more than three subparts of a question uploaded than…

Q: What is a sequence? What notation do we use to denote the terms of a sequence?

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Q: 2. The third term of an arithmetic sequence is x and a, = 19x + 6. Find the twelfth term. 3. Php…

A: given

Q: What is the sum of the first 145 terms in this sequence? 25, 21, 17, 13,...

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Q: 3. In an arithmetic sequence if 5th term value is 26 and 10th term value is 51. Find 15th term…

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Q: The first four terms of a sequence are given: 23, 21, 19, 17..., find the 50th term of the sequence.

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Q: Which geometric sequence has a first term equal to 55 and a common ratio of -5?

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Q: What is the 5th term of the geometric sequence 3/20, 3/2, 15, …? Show your solution.

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Q: What is the general formula and the 40th term of the linear sequence -6, 1, 8, 15, 22, ...

A: The linear sequence is -6,1,8,15,22......

Q: The first four terms of an arithmetic sequence are given. 27, 32, 37, 42, .. What is the 60th term…

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Q: What is the 75th term of the sequence given by 81,75,69,63

A: The given sequence is: 81, 75, 69, 63, ....

Q: Find the 53rd term of the arithmetic sequence 27, 11, -5, ...27,11,−5,...

A: The given arithmetic sequence is  27, 11, -5, ...............  The first term a = 27 difference d =…

Q: What is the 9th term of this sequence ?

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Q: Explain how to write a formula to describe the sequence 1, 3, 9, 27, 81, 243, Each term in the…

A: The given sequence is of a G.P. using G.P. common rato and first term we can easily find the n th…

Q: What is the 9th term of the sequence 6, 42, 294, 2058, ..?

A: First Term = 6 Second Term = 42 Third Term = 294 Fourth Term = 2058   Common Ratio = 42/6 = 7 The…

Q: Write down the nth term of the sequence suggested by the pattern. 12, 15, 20, 27

A: here is the solution:

Q: Which term of the geometric sequence 6, 18, 54, … is 118098

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Q: Find the 83rd term of the arithmetic sequence with 1st term 6 and common difference −1/2

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Q: The sequence 2, 6, 24, 120, . . .  is an example of a geometric sequence.Determine whether the…

A: Consider the given sequence 2, 6, 24, 120,.....

Q: What is the formula for this sequence and what is the nth-term of the sequence?…

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Q: What is the 103rd term of the sequence -32, -16, 0, 16, ...? O 1,600 O 1,632 O -1, 664 84,048

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Q: What is the first term of a geometric sequence which fourth term is -40 and with common ratio of -2?

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Q: Which arithmetic sequence has a first term equal to 47 and a common difference of -18?

A: To find the arithmetic sequence

Q: What is the sum of the first 47 terms of the sequence? −215,−201,−187,−173,

A: We have given a sequence  -215 , -201, -187, -173 So first term,a = -215 Common difference = Second…

Q: {3, 6, 12, 24, 48, 96, 192 } How do I find the explicit formula for this sequence?

A: Given sequence is 3,6,12,24,48,96,192 To find the explicit formula. Solution: Here, we have a1=3…

Q: 2) 2, 4, 64, 128

A: Given geometric sequence is 2, 4,__, __,__64, 128

Q: The 9th term of an arithmetic sequence is 19 and the 20th term is 20.3 What are the first three…

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Q: The first three terms of a geometric sequence are as 64, 32, 16 Find the next two terms of this…

A: Geometric Series: The general geometric series is in the form of a,ar,ar2,ar3,… where a is the first…

Q: The city animal shelter housed 36 animals in the year 2000. Every year, the number of animals…

A: Given problem:- The city animal shelter housed 36 animals in the year 2000. Every year, the number…

Q: What is the 11th term of the geometric sequence −1.5,−3,−6,−12,…?

A: Given series ,-1.5 , -3 , -6 , -12 ,---first term , a1=-1.5Common ratio , r=-3-1.5=2

Q: Write the first six terms of the arithmetic sequence with the given properties. 20th term is  −47;…

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Q: Determine which sequence is not an arithmetic sequence. 10, 6, 2, -2, ... 0, 0.5, 1, 1.5, ... о-7,…

A: topic - arithmetic sequence

Q: An arithmetic sequence has a first term of 0 and a 9th term of 12. Which term number corresponds to…

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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: )In the sequence 2, 5 , 8, 11, 14, .. , the common, =) In the sequence 2, 5, 8, 11, 14, .. , the…

A: Given query is to find the value of indicated terms.

Q: Explain how to write a formula to describe the sequence 1, 3, 9, 27, 81, 243, . Each term in the…

A: The given series can be written as, 1,3,9,27,81,243,.....  = 30,31,32,33,34,35, .... So, the given…

Q: term in a geometric sequence whose 3rd term is 5/4 and 6th term is 10?

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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.