(a) Given the recursive sequence aķ = ak-1 - k? +1 for all k > 1, and a1 = -4, find a2 and аз- (b) Compute the following sums using formulas from class. Do not try to compute something like 224. You may leave your answer in terms of big numbers like this. i. –23 + (-23)² +(-23)³ + ··. +(-23)1 75 ii. >ak if ar = 2k – 3 for all k > 1. Hint: Use properties of sums. k=1

Q: (b) Compute the following sums using formulas from class. Do not try to compute something like 224.…

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Q: Find the explicit formula for this polynomial sequence: 3, 24, 79, 180, 339, 568, 879, ..

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

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Q: Evaluate the sum 5+10+20+40+80+...+320, and enter its numerical value.

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Q: Given the recursive sequence ak = (12-06-1) ² - 1 ak-1 -k² + 1 for all k ≥ 1, and a₁ = -4, find a₂…

A: As per the guidelines I am answering only first question. Also note that while uploading for the…

Q: (X) 16 (D) 16 (E) 256 26. The sequence A is defined by A 100 terms in sequence A? A +2 for each…

A: Given, A_1=45 and An=A_(n-1)+2. Using n=2,3,4,.. in this expression we get: A_2=47,A_3=49,A_4=51,...…

Q: Example: Find the sum in 12 - hour clock arithmetic (a) 7 + 8 (b) 11 + 3

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Q: If all tems except ys of the sequence Y1» Y2» Y3. Y9 be given , show that the value of ys is 56 (y4…

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Q: I am trying to confirm my answer for a recursive sequence homework problem at University. I need to…

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Q: this sequence 31 27 23 19 Explain in detail how you could find the 10th term

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Q: The first term ao of a geometric sequence is -10, and the common ratio r is -3. What is the…

A: The formula for the nth term of a geometric sequence is given by an=a0rn-1, where a0 is the first…

Q: What is the sum 1+2+4+8+...+512?

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Q: Fred opens an account with $2500. Each month, the balance in Fred’s bank account earns interest so…

A: Given- Fred opens an account with =$2500 New balance after interest = 1.003 times the previous…

Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: If the sum 5+ 5(3)+5(3)² +...+5(9)* =5465 then the value of k is (a) 5 (b) 6 (c) 3 (d) 4

A: We know that 1+a+a2+a3+…+an-1=an-1a-1, if a≠1

Q: Which of the following would be divisible by 7? (A) x+ 7 (B) 7x + 1 (C) 14x + 21 (D) 77x +11 O A О в…

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Q: 51. The figures below are similar. What are a) the ratio of the perimeters and b) the ratio of the…

A: We use properties of similar figures.

Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: Use the formula for the sum of the first n integers to evaluate the sum given below, then write it…

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Q: For the sequence {an} defined recursively by a₁ = 1, a2 = 1, An+2 an+2 +an+1 for n > 2 Write a 44

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Q: recursively defined sequence

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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.