3. (6 pts) A sequence A = [a1, a2, . . . , anjis called a valley sequence if there is an index i with 1 < t < n such that al > a2 > . . . > ai and ai < ai+1 < . . . < an. A valley sequence must contain at least three elements. (a) (2 pts) Given a valley sequence A of length n, describe an algorithm that finds the element a, as...
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Question 15 < > B0/1 pt 53 99 0 Details Write down the first five terms of the following recursively defined sequence. aj = 3; an+1 2an + 10 Question Help: D Video Submit Question Question 16 < > 10/1 pt 5 3 399 0 Details For the sequence an = an-1 + an- 2 and aj = 1, a2 = 2, its first term is ; its second term is . its third term is . its...
The input consists of n numbers a1, a2, . . . , an and a target value t. The goal is to determine in how many possible ways can we add up two of these numbers to get t. Formally, your program needs to find the number of pairs of indices i, j, i < j such that ai+aj = t. For example, for 2, 7, 3, 1, 5, 6 and t = 7, we can get t in two...
6. Show that if A1, A2, ... is an expanding sequence of events, that is, AC A₂C...... then P(ALU AQU....) = lim P(An). 1-00
Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the nth term of the sequence as a function of n. (nth term formula: An = a1(r)-1) 1 a1 = 625, ak 11 = 5 -ak aj = a2 a3 = 04 = Preview 05 Preview r = Preview an = Preview Find the 6th of the geometric sequence: {64a( – b), 32a( – 36), 16a( – 96), 8a( – 27b), ...} an...
If the 100th term of an arithmetic sequence is 290, and its common difference is 3, then its first term a1 = ___________________ its second term a2 = __________________ its 3rd term a3 = ____________________
: Let a1, a2, a3, . . . be the sequence of integers defined by a1 = 1 and defined for n ≥ 2 by the recurrence relation an = 3an−1 + 1. Using the Principle of Mathematical Induction, prove for all integers n ≥ 1 that an = (3 n − 1) /2 .
Problem (5), 10 points Let a0:a1, a2, be a sequence of positive integers for which ao-1, and a2n2an an+ for n 2 0. Prove that an and an+l are relatively prime for every non-negative integer n. 2n+an for n >0
Problem (5), 10 points Let a0:a1, a2, be a sequence of positive integers for which ao-1, and a2n2an an+ for n 2 0. Prove that an and an+l are relatively prime for every non-negative integer n. 2n+an for n >0
This Question: 1pc Write the first six terms of the arithmetic sequence with the given first term, ay, and common difference, d a = -3, d=8 The first term of the sequence is a, = (Simplify your answer.) The second term of the sequence is az = (Simplify your answer.) The third term of the sequence is ag = 0 (Simplify your answer.) The fourth term of the sequence is at - (Simplify your answer.) The fifth term of the...