b) a_n = 5 + 2n . Web4 Answers Sorted by: 1 Let > 0 be given. Volume I. We can see this by considering the remainder left upon dividing \(n\) by \(3\): the only possible values are \(0\), \(1\), and \(2\). Determine whether the sequence converges or diverges. Find k given that k-1, 13, and 3k+3 are consecutive terms of an arithmetic sequence. 19. The terms of a sequence are -2, -6, -10, -14, -18. Answer 1, contains which literally means doing buying thing, in other words do shopping.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'jlptbootcamp_com-box-4','ezslot_7',105,'0','0'])};__ez_fad_position('div-gpt-ad-jlptbootcamp_com-box-4-0'); Answer 2, contains which means going for a walk. Find the general term and use it to determine the \(20^{th}\) term in the sequence: \(1, \frac{x}{2}, \frac{x^{2}}{4}, \ldots\), Find the general term and use it to determine the \(20^{th}\) term in the sequence: \(2,-6 x, 18 x^{2} \ldots\). Let #a_{n}=n/(5^(n))#. Simply put, this means to round up or down to the closest integer. Find an expression for the n^{th} term of the sequence. Approximate the total distance traveled by adding the total rising and falling distances: Write the first \(5\) terms of the geometric sequence given its first term and common ratio. 1, 3, \frac{9}{2}, \frac{9}{2}, \frac{27}{8}, \frac{81}{40}, (A) \frac{77}{80} \\(B) \frac{79}{80} \\(C) \frac{81}{80} \\(D) \frac{83}{80} \\(E) \frac{87} Find a formula for the nth term of the sequence in terms of n. 1, 0, 1, 0, 1, \dots, Compute the sum: \sum_{i \in S} \left(i^2 + 1\right) where S = \{1, 3, 5, 7\}. sequence Write the first or next four terms of the sequence and make a conjecture about its limit if it converges, or explain why if it diverges. s (n) = 1 / {n^2} ({n (n + 1)} / 2). -6, -13, -20, -27, Find the next four terms in the arithmetic sequence. The series associated with this is n=1 a n, where a n is the n th prime number. a_7 =, Find the indicated term of the sequence. Multiplying both sides by \(r\) we can write, \(r S_{n}=a_{1} r+a_{1} r^{2}+a_{1} r^{3}+\ldots+a_{1} r^{n}\). Let S = 1 + 2 + 3 + . If it converges, find the limit. For example, the following are all explicit formulas for the sequence, The formulas may look different, but the important thing is that we can plug an, Different explicit formulas that describe the same sequence are called, An arithmetic sequence may have different equivalent formulas, but it's important to remember that, Posted 6 years ago. In this form we can determine the common ratio, \(\begin{aligned} r &=\frac{\frac{18}{10,000}}{\frac{18}{100}} \\ &=\frac{18}{10,000} \times \frac{100}{18} \\ &=\frac{1}{100} \end{aligned}\). WebVIDEO ANSWER: Okay, so we're given our fallen sequence and we want to find our first term. (b) What is a divergent sequence? Predict the product from the reaction of substance (reddish-brown = Br) with Br_2, FeBr_3.