103. PROVE: Logarithms of a Geometric Sequence If a,, az, az, ... is a geometric sequence with a common ratio r>0 and a, >0, show that the sequence log a, log az, log a, . .. is an arithmetic sequence, and find the common difference.

Q: 5. The sum of the first n terms of a sequence is called the nth sum and is denoted by S.

A: An arithmetic sequence is a series of numbers that have the same common difference and the sum of…

Q: Suppose that the sequence {a}, is =1 1,3, 5, 7,9, 11, 13, .. Find the sum s=E k=1

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Q: 9. Find a formula for the general term an of the sequence: {1,0,1,0,1,0,1,0,...}

A: Given sequence is  { 1,0,-1,0,1,0,-1,0,....} Now we give formula of this sequence

Q: 11. Define what it means for a sequence {ak} to be eventuallystrictly increasing.

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Q: 1. Find the first four terms of the sequence whose nth term is an = 2 + 3n. * 5, 7, 9, 11 O -1, -4,…

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Q: 16.Consider the first 3 terms of the sequence a, (where k 2 2). A. Give the first 3 terms of the…

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Q: 13. Define what it means for a sequence {ak} to be eventuallystrictly decreasing.

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Q: 3 if it exists. 8 Find the infinite sum of the geometric sequence with a = 6, r = Preview

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Q: PROVE: Reciprocals of a Geometric Sequence If a,, az, az, ... is a geometric sequence with common…

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Q: What's the difference between an arithmetic and g eometric sequence? How do you find the general…

A: What's the difference between an arithmetic and geometric sequence? How to find the general terms of…

Q: Suppose that a sequence is defined as follows. a=2, a,=-3a,-1 for n22 List the first four terms of…

A: Given :              a1 = 2              an = -3 an-1 + 5 To find :                    The first…

Q: Let (a,) be the sequence defined by a¡ = 5 and a, = 2a,-1 – 3 when n > 2. What is a4?

A: Here an be the given sequence which is defined by a1=5 and an=2an-1-3 when n≥2 . We have to find a4…

Q: True or False For a geometric sequence with first term aj and common ratio r, where r + 0, r + 1,…

A: Let geometric sequence is a1,a1r,a1r2,a1r3...........a1rn-1 where a1 is the common difference and r=…

Q: The Fibonacci number is a sequence which is described explicitly by Fn = Fn-1 + Fn-2-

A: Given statement is The Fibonacci number is a sequence which is described explicitly by  Fn = Fn-1 +…

Q: Find an explicit formula for the general term an of the sequence. (1,-1/3,1/5,-1/7,...)

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Q: Show that the sequence +o0 is eventually strictly increasing or eventually strictly decreasing. an+1…

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Q: 9 16 2' 3' 25 What is the 30th term of the sequence 4, -- -

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Q: 4. (a) If (Cn)1 is the sequence Cn := ntn-2, compute lim,,0 Cn, sup{cn :n E N}, n2 and inf{cn : n e…

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Q: The first two numbers in a sequence H are H(1)=2 and H(2)=6. If H is an arithmetic sequence, write…

A: Given : H1 = 2H2 = 6 H is an arithmetic sequence.

Q: 4) Find x if the sequence 3, 6, 2x+5, is a) arithmetic b) geometric.

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Q: Suppose that a job offers a starting salary of $75,000 with a raise of $4000 every year thereafter.…

A: Given a starting salary of $75,000 with raise of $4000 every year

Q: (c) Show that the sequence is eventually strictly increasing. 13 n=1

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Q: 2.) Write the general formula for un for the arithmetic sequence 12, 4, –4, –12, ...

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Q: Is the limit of the ratio of any two successive increasing terms of the Fibonacci sequence.

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Q: Use the difference an+1-an to show that the sequence {n-9"} is strictly increasing or strictly…

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Q: Let {a,} be an infinite sequence with the property that 0 < a, < for all n 2 1. Calculate lim,-00…

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Q: 1 and the recursive Which sequence could be described by the first term: aj 2 definition: An+1 =…

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Q: 15. Find the 5th term of the geometric sequence whose common ration is and whose first term is 7.

A: Given first term is 7 and common ration is 1/2 Here a=7,r=1/2

Q: - Find x such that x, x+2, and x + 3 are consecutive terms of a geometric sequence. - Initially, a…

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Q: Use the difference anti-an to show that the given sequence {a} is strictly increasing or strictly…

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Q: Determine whether the sequence is increasing, decreasing, or not monotoni 7n – 8 an 8n + 2

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Q: ). Find the sum of the finite arithmetic sequence below. Sum of the integers from −100 to 60 −4,…

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Q: Suppose that a sequence is defined as follows. a1=-5, a,=4a, +10 for n>2 List the first four terms…

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Q: 4 if it exists. 8. Find the infinite sum of the geometric sequence with a = 5, r = I.

A: The infinite sum of the geometric sequence with the first term ''a'' and common ratio r  is   .…

Q: Suppose b1, b2, ba,.. is a sequence defined as follows. Show that 5 b, for all integers n > 0. bị =…

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Q: The tenth term of an arithmetic sequence is 23, and the second term is. Find the first term. X

A: Let's find first term of arithmetic sequence.  Tenth term = 73/2 Second term = 9/2

Q: Suppose that al, a2, a3, .. is an arithmetic sequence with common difference d. Show that 10, 10,…

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Q: 1. - Determine whether the sequence is arithmetic, geometric, or neither. 1 1 1 1 2'3'7'5'* 2.…

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Q: the n^th term of the following sequence 1,4,7,10,...is

A: For given sequence a1 = 1 a2= 4 a2 = a1 + 3

Q: 1. If the first three terms of an arithmetic sequence are k - 2, 2k +1 and k + 2, find the value of…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let the arithmetic sequence be defined by the formula un=11+(n - 1) x 6 Apply the concepts of the…

A: An arithmetic sequence is a set of numbers that obey a specific mathematical expression called its…

Q: The "Tribonacci" sequence is the sequence defined by To = T1 = T2 =1 and %3D Tn+3 = Tn + Tn+1+Tn+2…

A: The ''Tribonacci'' sequence is the sequence defined by,  T0=T1=T2=1 and Tn+3=Tn+Tn+1+Tn+2

Q: Show that if a and x are any two nonzero real numbers, then ,-1,,-.. is a geometric sequence.

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Q: e) Suppose {a,}nEN is a sequence defined by a, = (a) Show that a, = 3- an-1+ 2. (b) Find (dn -…

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Q: 1. If the numbers a, m,m2, C, m, b form an arithmetic sequence, we say that the numbers m,m2, C, m…

A: If there are k arithmetic mean between a = 1 and b = 30 and d is the common difference of the…

Q: Give a recursive definition of the sequence {an}, n = 1, 2,... if: a. an=4n-2 b. an=1+ (-1)"

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Q: Consider the following sequence. 54, 18, 6, 2, ... State the general expression for the nth term of…

A: Find out common ratio of given expression,d= 1854,618, 26=13Therefore ,Given expression is geometric…

Q: Determine whether the sequence {5n−7 / 3n+4} is increasing, decreasing, or neither.

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Q: 7. Let a1, a2, a3, ... be a geometric sequence with initial term a and common ratio r. Show that af,…

A: Given that a1, a2, a3, ⋯ be a geometric sequence with initial term a and common ratio r. That is,…