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can you do number 18???
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- 00 {(-) 4. Give the LUB of the sequence: 2 n=1 а. 1/2 b. 1/4 с. -1/4 d. -1/2 е. О30. Ifx', 4x + 3, 25 are in geometric sequence, find the values of x. а. -1/3 b. 1/3 or -3 с. -3 d. -1/3 or 3Determine the limit of the sequence, or state that the sequence diverges. Show the reason to support your answer. 1 (a) an = (-1)". n2 + 1 (b) ап arctan(-3n). en (с) ап n2 (-). (d) an = 3
- Write out the first five terms of the sequence, determine whether the sequence converges, and if so, find its limit. 3. +∞ Inn (1^²)+1=1 n n=1 4. {n²e-n}+1Write out the first five terms of the sequence , determine whether the sequence converges, and if so find its limit. [(-1)*-1 ¯ (n+4) . n=1 Enter the following information for an = (-1)"-1 (n+4)² · = Ip a2 = аз a4 A5 = (-1)"–1 lim (n + 4)² Does the sequence convergeFind the limit of the sequence. {v2, /2v2, V 2/2/2,...}
- 2. Find the limit of the sequence a1 = V2, a2 = V2v2, az = /2V2v2, a4 = 2/2/2v2,...3. Determine whether the sequence is monotonic. Prove you are correct. (a) {n²} 1 (b) lyn +2 » {1. "} (d) {} (c) (-1)" } 2n n (e) n +1] (-1)" \ (f) 3nCalculate, to four decimal places, the first ten terms of the sequence. ¹ + (- - -) " = 1 + 1 2 3 4 5 6 7 8 9 10 Using the calculations above, plot the graph of the sequence. y 1.0 0.5 -0.5 -1.0 y 1.10 1.05 0.95 0.90 an . 2 4 6 Does the sequence appear to have a limit? Yes No If so, calculate it. If not, enter DNE. 8 10 X y 1.0 0.5 -0.5 0-1.0 y -0.90 -0.95 -1.00 -1.05 -1.10 . 2 4 6 8 10 X
- E. In a sequence: a1 — 3, аз — 7, and a, 2ап-1 + аn-2 for n > 3. (12) Find aҙ- (13) Find a4.Find the limit of the sequence {an} = { V 6n - }. Enter as an exact value. V4n+1 lim, >o help (numbers) n→∞ An IFind the limit of the sequence if it converges; otherwise indicate divergence. a, =7+ (0.9)", for n= 1, 2, 3, .. О А. 7.9 О В. 8 Ос. 7 O D. Diverges