Show that the sequence is geometric by showing the ratio of successive terms is a nonzero constant. 6h-1 tn -1 = %3D (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.) What is the value of the common ratio? |(Type an integer or a simplified fraction.) What is the value of the first term? (Type an integer or a simplified fraction.) What is the value of the second term? (Type an integer or a simplified fraction.) What is the value of the third term? (Type an integer or a simplified fraction.) What is the value of the fourth term? | |(Type an integer or a simplified fraction.)

Q: Four distinct positive integers a, b, c, and d form an arithmetic sequence. Also, the integers a, b,…

A: If we have an arithmetic sequence, then it is of the form n, n+m , n+2m, n+3m, .... Here n is the…

Q: The first term of an arithmetic sequence is 5. The third term of the sequence is 13. Which of the…

A: Given,First term of AP = a = 5Third term of AP= 13Let, Second term of AP = xWe can write AP as - 5,…

Q: A partial sum of an arithmetic sequence is given. Find the sum. 3 + 6 + 9 +... + 324

A: 3+6+9+...+324 the first term is  a1=3 find the common difference d=6-3 d=3 . and the last term is…

Q: Find the common difference and the sum of the first 5 terms of the arithmetic sequence. an = 5n – 2

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Q: Find the nth term of the arithmetic sequence (a,) whose initial term a and common difference d are…

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Q: Find the 65th term of the arithmetic sequence with first term 3 and common difference -1/2 (negative…

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Q: Find the nth term of the arithmetic sequence {a,} whose initial term a and common difference d are…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: The given series is: 7,8,9,10,11,... So, the first term of the series is: a1=7 which can be written…

Q: A partial sum of an arithmetic sequence is given. Find the sum. 0.9 + 3.9 + 6.9 + . . . + 78.9 S =

A: Partial sum of an arithmetic sequence is given as- 0.9+3.9+6.9+. . . +78.9 To find the sum S. Here…

Q: Find the nth term of the arithmetic sequence {a,} whose initial term a and common difference d are…

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Q: Find the term ag for the geometric sequence with first term, a, = 4, and common ratio, r= 3 ag (Type…

A: The solution is given as

Q: Show that the sequence is arithmetic. Find the common difference, and write out the first four…

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Q: Write a recursive formula for the sequence represented by the explicit formula. 1 an 5(4)n-1…

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Q: %3D

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: The first term of an arithmetic sequence is -4. The fifth term of that arithmetic sequence is 16.…

A: Given: The first term of the arithmetic sequence is -4, i.e. a=-4.            The fifth term of the…

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: Consider the geometric sequence defined by an=3 (2) n–1 1. Find the first four terms of the…

A: The given geometric sequence is: an=3×2n-1

Q: Consider the sequence whose nth term is an = 4n - 3. Find a2 - a1, a3 - a2, a4 - a3, and a5 - a4.…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: Given: The sequence is 32,34,38,316,332,... To determine: The first term and formula for the general…

Q: Show that the given sequence is geometric. Then, find the common ratio and write out the first four…

A: Given en=4n-18Here we show that en=4n-18 is a sequence of geometric . Thenfind the common ratio…

Q: Find a formula for.the general term an of the sequence assuming the pattern of the first few terms…

A: Given first few terms of a sequence  To find the an  term

Q: Show that the given sequence is geometric. Then, find the common ratio and write out the first four…

A: Given sequence is Sn=6n

Q: Which arithmetic sequence has a common difference of -21?     A   {1,245; 1,224; 1,203; 1,182; …}…

A: Given, The arithmetic sequences  (A) 1,245; 1,224; 1,203; 1,182; …....  (B)  1,563; 1,587; 1,611;…

Q: Show that the sequence is arithmetic. Find the common difference, and write out the first four…

A: Solution is given as below:

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indica Find…

A: For geometric series : given : put values :

Q: What is a recursive definition of a sequence?

A: A recursive sequence is a sequence in which terms are defined using one or more previous terms which…

Q: Determine if the sequence below is arithmetic or geometric and determine the common difference /…

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Q: Find the common difference d and the nth term a, of the arithmetic sequence whose 7th term is 2 and…

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Q: f the second and third terms of a geometric sequence are 108 and 36, what is the first term? Express…

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Q: Write a recursive formula for the sequence represented by the explicit formula. a, = 8.2(8)n - 1…

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Q: rite a rule for the n​ th term of the geometric sequence. Then identify the first six terms o

A: Here we have fifth term of G.P = a5=162 The common ratio r=-3 Let first term =a

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: Find the 75th term of the arithmetic sequence with first term 2 and common difference -1/2.

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Q: Determine if the sequence below is arithmetic or geometric and determine the common difference /…

A: The given sequence is 125,25,5,... To determine if this sequence is arithmetic or geometric and…

Q: Modern Car Company has come out with a new car model. Market analysts predict that 3600 cars will be…

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Q: Gxplan why an =E convenges as Sequence, but diverges as series.

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: The given sequence is:  8, 7, 6, 5, 4, ...

Q: What is the explicit rule for the nth term of the geometric sequence? 3, 18, 108, 648, 3,888, O an =…

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Q: Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic,…

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Q: The first three terms of a geometric sequence are lnx16, lnx 8, lnx 4, for x > 0. Find the common…

A: Here given three terms in geometrical sequence. We have to calculate common ratio.

Q: 24 Use a graphing calculator to find the first 10 terms of the sequence an = n its 9th term is its…

A: We have to find

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: Solving the problem by finding the n th term of the given sequence.

Q: The first term of a geometric sequence is 15, and the 5th term of the sequence is 243 What are the…

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Q: Determine whether the sequence is arithmetic, geometric or neither. Select an answer v 0.125, -0.5,…

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Q: Consider the sequence whose nth term is an = 4n - 3.Find a2 - a1, a3 - a2, a4 - a3, and a5 - a4.…

A: an=4n-3. Put n=1, 2, 3, 4, 5 in an=4n-3, we get a1=41-3=1a2=42-3=5a3=43-3=9a4=44-3=13a5=45-3=17

Q: Find the indicated term of the geometric sequence whose initial term and common ratio are given.…

A: Topic - geometric serquence Note : as per bartleby Guidelines, we are supposed to answer only first…

Q: It is given that three positive integers form an arithmetic sequence. Find these three integers if…

A: Let the three integers be a-d, a and a+d.

Q: A partial sum of an arithmetic sequence is given. Find the sum. 3+8 + 13+. . . +538

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Q: Provide a Geometric Sequence, by either giving a General rule or explicitly listing the first five…

A: the general form of a geometric sequence is: a,ar,ar2 ,ar3 ,ar4 ,..... The nth  term of a geometric…

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.