Use the following pattern to complete parts (a) and (b) below  19+57=19•2^2 19+57+95=19•3^3 19+57+95+133=19•4^2   a. Conjecture a generalized based on this pattern  choose the correct answer a. The sum of the term is 19n b. The sum of the terms is 19(n+1) c. The sum of the terms is 19n^2 c. The sum of the terms is 19•2^n+1   b. Based on the generation in (a) find the sum of the sequence 19+57+95+133+....+247 the sum of the sequence is _

Q: What is a formula to calculate the sum of the first n positive integers? Could you explain why this…

A: Obtain the sum of first n positive integers as follows.The general formula to calculate the sum of…

Q: Find the sum of the first 12 terms of the geometricsequence with first term 48 and common ratio1/2.

A: The geometric sequence is the sequence which is of the form a,ar,ar2,ar3,......  , where a is the…

Q: 2n+2 Σ (3k + 2n) k=0 = 11 first step 2nd step 3rd step final answer

A: The given summation is                          ∑k=02n+2(3k+2n)

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A: Consider the given information as a=-4 and d=2

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

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Q: Express the sum 3 + 5 + 7+ ... + (2k-1) using E-notation.

A: The given sum is 3+5+7+…+2k-1. Express the sum 3+5+7+…+2k-1 using ∑ notation as follows.

Q: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: If 17th term of an AP exceeds its 10th term by 7 , Find the common differenc

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Q: Find the Sum to infinity of the sea tès - Ce30 t ces 20 - 1-3 1-3.5 ces 30 + - (-nCBCIT). 2.4 2.4-6

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Q: The ration of the sums of m and m terms of an AP is m2:n2 .show that the ratio of mth and nth  is…

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Q: Find the sum of first 24 terms of the list of numbers whose nth term is a, = 3 + 2n

A: Introduction :

Q: Find the sum of first 20 terms of an AP in which 3rd term is 7 and 7th term two more than thrice of…

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Q: What is the summation from n = 1 to infinity, of  (3n+1) / (5n + 4) ?

A:

Q: Express the sum in terms of summation notation. (Answers are not unique.)

A: To express: The sum in terms of summation notation: Given: The sum is 14-112+136-1108. Calculation:…

Q: find a simple recursive definition of the sequance with general term tn=2(n-1)+7 for n>2

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Q: 1. Find the 12th term of 8, 3, -2,...

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Q: Needing help finding the partial sum of the equation in the attached image.

A: The correct option is (d).First of all, consider the given expression.Then apply the sum rule on the…

Q: The 11th termof an A.P. exceeds than 10h term by 7 find the commondifference.

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Q: 6. Use the trapezoid rule with n = 150 to approximate 5 dr. You need to carefully write out 1+ a the…

A:

Q: :The nth term formula for { 1,0,1,0,... } is

A: given sequence 1, 0, 1, 0, .........

Q: Find the sum of the even integers between 35 and 49. The sum is ...

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Q: Express the sum in terms of summation notation. (Answers are not unique.)4 + 11 + 18 +....+ 466

A: Our Aim is to express the sum 4+11+18+.....+466 in terms of summation notation.

Q: Express the sum in terms of summation notation. (Answers are not unique.)3 + 8 + 13 + ....+ 463

A: Arithmetic progression is a sequence of numbers in which the difference between two consecutive…

Q: 3. Multiply out writing the result in summation notation.

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Q: Express the following sum in closed form. Σ 2 k > (4 +3 in k=1 -(+-2 ). k Hint: Start by multiplying…

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Q: 20 j ΣΣ (2k + 3) = j=5 k=0 = 2n+3 Σ (n + 5k)3 k=0 first step 2nd step final answer first step and

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Q: Determine how many terms of (-1)*+lgk must be summed to be sure that the remainder term k! k=1 is…

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Q: Can you use polynomial fitting to find the formula for the nth term of the sequence 4, 7, 11, 18,…

A: No. The sequence of differences is the same as the original sequence so no differences will be…

Q: Find the sum of the first 12 terms without adding them all up. Explain your reasoning and show your…

A: follow next step

Q: Which numbers in Z17 are relatively prime to 17? Enter your answer as a comma separated list of…

A: The objective of the question is determine all al relatively prime to 17 in Z17 .

Q: Find the sum of the first 15 terms of the geometricsequence with first term 3 and common ratio 2.

A: To find the sum of the first 15 terms of the geometricsequence with first term 3 and common ratio 2.…

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a. 3+2n

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Q: Use summation notation to rewrite 15-3+3/5-...-3/625

A: A series represented in compact form is called summation notation.it is represent by the Greek…

Q: Express the sum in terms of summation notation. (Answers are not unique.)2 + 4 + 8 + 16 + 32 + 64 +…

A: To express: The sum in terms of summation notation: Given: The sum is 2+4+8+16+32+64+128.…

Q: Find the sum. 1 - 1- 14 - 196 - 2744 -.. - (14)"- Sn =| (Simplify your answer.) !!

A:

Q: Express the sum in terms of summation notation. (Answers are not unique.)3 + 8 + 13 + 18 + 23

A: Given sequence is 3+8+13+18+23. To express the sum in terms of summation notation. Solution:…

Q: Find the sum of the first 10 terms of the geometricsequence with first term 5 and common ratio -2.

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Q: composite. 10. Suppose that n = 2³ x 5² × 7 × 17³. Give the prime factoriz= (Hint: Do not work too…

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Q: 7, Evaluate the integral Express numbers in exact form.use symbolic notation and fractions where…

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Q: Calculate the sum  10 (18ak − bk)   k = 1  assuming that  10 ak   k = 1 = 210 and  10 bk   k = 1 =…

A: Given data is: ∑k=110ak=210  and  ∑k=110bk=249

Q: 22. Without expanding the power, what is the yf term in the expanded form of (x- 2y)? Show your…

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Q: If the 6th term of a GP is 9375 and it's 4th term is 375.find the 9th term

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Q: Find two positive integers such that the four times loo0 and the product large as possible. the .…

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Q: Find the sum of first 30terms of an ap whose second term is 2 and seventh term is 22

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Q: Find the first 5 terms in the sequence. 3.) x + 9 -8,-7,-6,-5,0 A.) י5n1 -7,-2,3,

A: First five terms of sequence

Q: Use the trapezoid rule with n= 150 to approximate 1+744. You need to carefully write out the sums in…

A: Trapezoidal rule:  where n=150 and Now, the given integral is

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a = 3 + 2n

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given expression: 3c+c247 Concept used for the general term:…

Q: Express the sum in terms of summation notation. (Answers are not unique.)

A: a0+a1x4+a2x8+----+a25x100 It can be written as,…

Q: Use sigma notation to write the sum. [6 - ()°] + [6 - (4)°] +-- • [s - (2)'] k = 1

A: According to the problem, we have

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.