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260, 130, 120, 60,__ ,__, A definite relationship exists among the numbers in the series. 1, 3, 5, What is the sum of the 2nd, 7th, and 10th terms for the following arithmetic sequence? This is n(n + 1)/2 . Volume I. a_n = (-(1/2))^(n - 1), What is the fifth term of the following sequence? 30546 views What is the 4th term of the sequence? Given that \frac{1}{1 - x} = \sum\limits_{n = 0}^{\infty}x^n if -1 less than x less than 1, find the sum of the series \sum\limits_{n = 1}^{\infty}\frac{n^2}{ - \pi^n}. 19. It is also commonly desirable, and simple, to compute the sum of an arithmetic sequence using the following formula in combination with the previous formula to find an: Using the same number sequence in the previous example, find the sum of the arithmetic sequence through the 5th term: A geometric sequence is a number sequence in which each successive number after the first number is the multiplication of the previous number with a fixed, non-zero number (common ratio). (Assume n begins with 1.) Determine whether or not there is a common ratio between the given terms. a_n = \left(-\frac{3}{4}\right)^n, n \geq 1, Find the limit of the sequence. What is the common difference of the sequence 1, 5, 9, 13, . a_n = \frac{1}{n +1} - \frac{1}{n +2}, Use the table feature of a graphing utility to find the first 10 terms of the sequence. If the limit does not exist, then explain why. WebAnswer: Step-by-step explanation: 3n +4 sequence. If the ball is initially dropped from \(8\) meters, approximate the total distance the ball travels. Similarly to above, since \(n^5-n\) is divisible by \(n-1\), \(n\), and \(n+1\), it must have a factor which is a multiple of \(3\), and therefore must itself be divisible by \(3\). What is the nth term of the sequence 2, 5, 10, 17, 26 ? are called the ________ of a sequence. Determine whether the following sequence converges or diverges. Determine whether the sequence is decreasing, increasing, or neither. Consider a fish population that increases by 8\% each month and from which 300 fish are harvested each month. If it is, find the common difference.