1) Find the sum of the first 10 terms of the sequence 4, 8, 12, 16, 20, ..

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: The sum of the first n terms of a sequence is given by S, = 3" +1 - 6 3.1. Determine the sum of the…

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Q: Fibonacci sequence

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Q: Can you find a formula or rule for the nth term of a se- quence related to the prime numbers or…

A: The formula for nth term of sequence for given problems are given in step 2.

Q: How many terms are there in each of the following sequences? a. 1, 3, 32, 33 3399 b. 11, 17, 23, 29,…

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Q: 5. Find the first five terms of the recursively defined infinite sequence: а, %3D 2, а, %3D5 & a,…

A: a1=2, a2=5 and ak+1=9ak-4ak-1

Q: Show that the sequence 9,12,15,18, ... is an AP. Find its 16th term and the general term.

A: We need to show that the sequence 9, 12, 15, 18, ... is an AP. Here, 12 - 9 = 15 - 12 = 3. And the…

Q: 2. Find the closed form for the generation function for the sequences (i) 2, -2, 2, -2, 2, -2, - - -…

A: The closed form for the generation function for a sequence is used to define the general term of a…

Q: The 1st, 5th, and 13th terms of an arithmetic sequence re the first three terms of  geometric…

A: Let the first term of arithmetic series be a0 So the fifth term is And the thirteenth term is   So…

Q: Terms of the sequence a1, a2, a3, ·.., a2020 are obtained by the rule: 1+ a2 1+ a2019 1+ a1 1- a1 az…

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Q: A sequence ao, a1, a2, .. .satisfies an = n an-1+(-1)" for n > 1. If a5 = 44, then az %3D

A: Since, a sequence a0,a1,a2,..... satisfies an=n.an-1+(-1)n-(i) for n≥1.Ifa5=44. Our Aim is to find…

Q: 5. The base of a right triangle right triangle is equal equal to the sum of the first ten,…

A: We need to find area, perimeter, hypotenuse.

Q: If you are going to fill up all the squares in a chessboard. By filling up the first square with…

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

Q: 52. Find the sum of the first 60 terms of the sequence. {2, 10, 18, 26,...}

A: Solution:Given      the sum of the first 60 terms of the sequence{2,10, 18, 26,...}FormulaSn=n2…

Q: Find the erplicit formula for the sequence 25, 5, 1, ,.

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Q: 1. What is the 21st term of the arithmetic sequence 19,14, 9, 4...? 2. Find three terms between 6…

A: according to our answering guidelines we can only answer 3 subparts at a time, rest you can repost…

Q: In each case, find the first 5 terms of the Sum and comgute S

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Q: The generating function of the sequence 4,4,4,4,4 is

A: # To find generating function of sequence  4,4,4,4,4,4 ??

Q: Terms of the sequence a1, a2, a3, . .. , a2020 are obtained by the rule: 1+a1 1+ a2 1+ a2019 az = 1-…

A: Reciprocal of a number n is 1n.

Q: Consider the sequence: 17, 14, 11, 8, ..., find the 26th term of the sequence.

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Q: 2n – the first six terms of the sequence defined by an = Зп + 1 az = Az =

A: Solution of the problem as follows

Q: Let Sn, be the sum of the first n terms of the geometric sequence 2, 6, 18, 54,.. 1. Express Sn in…

A: Given geometric sequence 2,6,18,54,...

Q: the

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Q: , n=1,2,3. is a sequence of real numbers defined by a, = /2 %3D %3D and for n21, a = 2,/2+a, .

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Q: A ternary digit is either 0, 1, or 2. How many sequences of nine ternary digits are possible…

A: The ternary digit is either 0 or 1 or 2.

Q: Construct a difference table to predict the next term of the sequence. 1, 4, 13, 28, 49, 76, . . .

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Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

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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: 1. Provide an Arithmetic Sequence, by either giving a General rule or explicitly listing the first…

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Q: The first six terms of the Fibonacci sequence are 1,1,2,3,5, and 8. 1. Write the first 12 terms of…

A: Fibonacci series goes like: xn=xn-1+xn-2The nth term of the series is sum of the previous two…

Q: If a sequence is unbounded, then it diverges. True or False?

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Q: A sequence a,,a,,a,,a, a of real numbers is such that Can the arithmetic mean of {a,,a,,a,) be less…

A: The arithmetic mean of the sequence a1,a2,a3,⋯an is defined by the formula, A.M.=a1+a2+a3+⋯+ann…

Q: Construct a difference table to predict the next term of the sequence. −1, 3, 21, 58, 119, 209,…

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Q: Find the formula of the Sequence. 1.) 2,1,3,4/3,15/4..., or 2, 2/2, 3/1, 4/3, 5(3)/4,...-

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Q: Determine whether each of the following statement about Fibonacci numbers is true or false. Note:…

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Q: 1. Find an explicit formula for the general term of the given sequence: 5, 10, 20, 40, 80,…..

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

Q: Using the appropriate formula,find the 17th term of the sequence 7,4,1,......

A: It is arithmetic progression

Q: Suppose that the sequence {az}ı is k=1 1,3, 5, 7,9, 11, 13,.. What is a1?

A: First we find the general of the given sequence {ak}∞k=1=1,3,5,7,9,11,13,..., with the help of…

Q: 3) Find three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a…

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Q: A sequence a1, a2, a3,.... satisfies the property that an+1 is the average of the first n terms if…

A: We have to find a2 .

Q: Consider the sequence: 2, 4, 8, 16, 32, ...Determine the 13th term of the sequence.

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Q: 7. What is the 12th term of the sequence 10, 6, 2, ...? O-16 O-24

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Q: Suppose we have the sequence 1, 4, 7, 10, ... Find an explicit formula for the nth term of the…

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Q: True or false? In the sequence: 10, 7, 4, ...., the initial term is 10 and the  tenth term is -20.…

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Q: Find an explicit formula for the general term  an  of the sequence. 1, −  1 3 ,   1 5 , −  1 7 ,…

A: We have to find the formula of general term.

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: Find the sum of the first 150 terms of the arithimetic sequence 6,9/2,3,........

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Q: Find a formula for thr nth term of the arithmetic sequence. 24,22,20,18,16, …

A: Given query is to find the nth term of the sequence.

Q: Determine whether the sequence is a​ Fibonacci-type sequence​ (each term is the sum of the two…

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Q: Find the sum of the first n terms of the arithmetic sequence.−9 + (−12) + (−15)+ ... (to 10 terms)…

A: It is an arithmetic series with  Now sum of the first n terms is,

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.