Four distinct positive integers a, b, c, and d form an arithmetic sequence. Also, the integers a, b, and d form a geometric sequence. If the sum of the.four integers is a perfect cube, what is the smallest possible value of a? Explain how you know this is the smallest possible value of a.

Q: Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75,…

A: First Term of the sequence is a1=15.75 common difference is: d=an-an-1=a2-a1=14.25-15.75=-1.5…

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: If the 100th term of an arithmetic sequence is 200, and its common difference is 2, then its first…

A: Given an arithmetic sequence100th term of this A.P=a100=200common  difference=d=2

Q: Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic…

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Q: Find the missing terms of the sequence and determine if the sequence is arithmetic,

A: Sequence is said to be geometric when it has common ratio and arithmetic when it has common…

Q: .A sequence can be generated by using an = a(n-1) + 6, where a = 3 and n is a whole number greater…

A: The given sequence is an=an-1+6 where a1=3. Put n = 2,  a2=a1+6=3+6=9 Put n = 3, a3=a2+6=9+6=15 Put…

Q: An arithmetic sequence is defined as consecutive terms that have a common difference. O True O False

A: NOTE: Refresh your page if you can't see any equations. . the nth term of the arithmetic sequence is…

Q: If the 100th term of an arithmetic sequence is 893, and its common difference is 9, then its first…

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Q: For an arithmetic sequence, a25 32. If the common difference is 1, find: a1 = the sum of the first…

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Q: Find the infinite sum of the geometric sequence with a = 2, r = 3 if it exists. -

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Q: Write a rule for the n th term of the geometric sequence for which a, = 64 and a,=1.

A: Solving by geometric sequence we have

Q: A sequence is shown in the graph. (1,6) 2 (2, 3) (3, 1.5) (4, 0.75)

A: Given Figure :-

Q: An arithmetic sequence whose first term is 2 has the property that its second, third, and seventh…

A: Given The arithmetic sequence whose first term is 2 has the property that its second, third, and…

Q: If the 100th term of an arithmetic sequence is 691, and its common difference is 7, then its first…

A: nth term of an arithmetic sequence is given by, an = a1+ (n - 1)d  where a1 is first term and d is…

Q: Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12.

A: Note:-  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Write a recursive formula for the arithmetic sequence bn given below. −14,−18,−22,−26,−30,…

A: We can solve this as follows:

Q: In an arithmetic sequence { 183, 160, 137, · · - ·}, the common difference is ...... 114 -26 -23 25…

A: We have to check

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

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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: If a1, a2, a3, a4, ... is a geometric sequence with common ratio r, show that and determine the…

A: Given  is a geometric series with common ratio r, so we have

Q: Which explicit formula describes the arithmetic sequence {19,14,9,4,...}

A: The arithmetic sequence is given by 19, 14, 9, 4, ····· To determine : The explicit formula of the…

Q: If the 100th term of an arithmetic sequence is 182, and its common difference is 2, then its first…

A: Given that the 100th term of an arithmetic sequence is 182 and its common difference is 2.

Q: The middle term of an arithmetic sequence equals 17, the last term = 32, and the fourth term = 11.…

A: Given middle term = 17 Last term = 32 Fourth term = 11 T4 = a+3d = 11 Middle term = T6 = a+5d = 17…

Q: Find the common difference and the sum of the first 8 terms of the arithmetic sequence. an = 4(n-1)…

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Q: An arithmetic sequence will always have a common ratio. O True O False

A: In an Airthmetic sequence the difference between one term and the next is a constant.We just add the…

Q: If the common difference of an arithmetic sequence is 4 and a(6 ) = 15, find the first term of the…

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Q: If the 100th term of an arithmetic sequence is 476, and its common difference is 5, then its first…

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Q: Write the arithmetic sequence – 5, – 8, – 11, – 14, ... in the standard form: - - an

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Q: In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the…

A: According to question given :-Series 3a, 3a2b, 3a3b2, 3a4b3...We have to find sixth term and  the…

Q: If 4x,x+2 and x-5 form in arithmetic sequence,what is the value of x?

A: Given         4x  , x+2 and x-5 from in arithmetic sequence.      Since   4x  , x+2 and x-5 are in…

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: An arithmetic sequence has a common difference equal to 10 and its 6th term is equal to 52. Find its…

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Q: The explicit formula of an arithmetic sequence is an =-4.5+6.5(n-1), what is the recursive formula?

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Q: Find the indicated term of the geometric sequence. 6th term of 3, 3/4, 3/16…

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Q: 1. If the expressions 3x+2, x^2,6x+3 whole numbers, find the value of x. forms an Arithmetic…

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Q: can a sequence be geometric and arithmetic?

A: Answer

Q: The sum of the first eight terms of an arithmetic sequence {an} is 24; the sixth term is 0. Find a…

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Q: How many terms are there in an arithmetic sequence with a common difference of 4 and with first and…

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Q: Is the sequence shown in the picture bounded? Why or why not? What work has to be done to show if a…

A: The given sequence is: an=1,4,7,10,.....  Given sequence is a arithmetic progression with: an…

Q: A test question lists the first four terms of a sequence as 2, 4, 6, and 8 and asks for the fifth…

A: Given sequence is: 2,4,6,8, Here we observe that: 4-2=26-4=28-6=2 Thus, we observe that each…

Q: Write an explicit formula for the nth term of the arithmetic sequence. Find the sixth and tenth…

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Q: What is an example of a real-world scenario that involves a sequence. Define the sequence in three…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Determine if the sequence is arithmetic. If it is, find the common difference, the explicit formula,…

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Q: If the 100th term of an arithmetic sequence is 600, and its common difference is 6, then its first…

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Q: If two terms of an arithmetic sequence are a₁₁ = 26 and 815 = -10, what is 828? -226 O-217 O-127…

A: I have stated the used formula in the solution.

Q: If the 100th term of an arithmetic sequence is 589, and its common difference is 6, then its first…

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Q: If the given sequence is an arithmetic sequence, find the common difference. If is not an arithmetic…

A: Given : Given sequence is 2,7,12,17,22,...   To Check: Given sequence is an arithmetic sequence or…

Q: and determine if the sequence is arithmetic, geometric, or neither 1/3, 1,3,9

A: In this question we will use basic of algebra i.e concept of sequence and series. Solution of the…