Answer question 42. Use summation equations. please write out the steps and describe in detail what you are doing during each step. -1700ofDetermine r and a₁ for each geometric sequence. See Example 3.V129. a3=5, ag =27. a2=-6, a = -192 28. a₂-8, a7 = 2566251110030. a4=7₁ ag =4¹31. a3 = 50, a1 = 0.00532. a3 = 300, a, =243128Use the formula for S, to find the sum of the first five terms of each geometric sequence.In Exercises 37 and 38, round to the nearest hundredth. See Example 5.33. 2, 8, 32, 128,...34. 4, 16, 64, 256, ...9 94 435. 18,-9,36. 12, -4,2² 439***37. a₁ = 8.423, r = 2.85938. a₁ = -3.772, r = -1.553Evaluate each sum. See Example 6.39.(-3)/40. Σ(-2)'41. 48 (¹)1=142.· 243 (²)43. 2445. Concept Check Under what conditions does the sum of an infinite geometric seriesexist?46. The number 0.999... can be written as the sum of the terms of an infinite geometricsequence: 0.9 + 0.09 +0.009+. Here we have a₁ = 0.9 and r= 0.1. Use theformula for So, to find this sum. Does intuition indicate that this answer is correct?Find r for each infinite geometric sequence. Identify any whose sum diverges.47. 12, 24, 48, 96,...48. 2,-10, 50, -250, ...X-S49. -48, -24, -12, -6, ...50. 625, 125, 25, 5,...Work each problem. See Examples 7 and 8.S51. Use lim S, to show that 2+1+ +++converges to 4.81852. We determined that 1 ++ 1 1++27converges to using an argumentlimits. Use the formula for the sum of the terms of an infinitoobtain the same resultܐ܂44.9

Answered: Image /qna-images/answer/18559fe3-d3b5-49d7-90f8-7df99f591091.jpg

Answered: 42. j=1 ¹3 (²) 243

Math

Advanced Math

42. j=1 ¹3 (²) 243

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter12: Sequences, Series And Binomial Theorem

Section12.3: Geometric Sequences And Series

Problem 12.44TI: Write the first five terms of the sequence where the first term is 6 and the common ration is r=4.

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Question

Answer question 42. Use summation equations. please write out the steps and describe in detail what you are doing during each step.

-1
700
of
Determine r and a₁ for each geometric sequence. See Example 3.
V
1
29. a3=5, ag =
27. a2=-6, a = -192 28. a₂-8, a7 = 256
625
1
1
100
30. a4=
7₁ ag =
4¹
31. a3 = 50, a1 = 0.005
32. a3 = 300, a, =
243
128
Use the formula for S, to find the sum of the first five terms of each geometric sequence.
In Exercises 37 and 38, round to the nearest hundredth. See Example 5.
33. 2, 8, 32, 128,...
34. 4, 16, 64, 256, ...
9 9
4 4
35. 18,-9,
36. 12, -4,
2² 4
3
9***
37. a₁ = 8.423, r = 2.859
38. a₁ = -3.772, r = -1.553
Evaluate each sum. See Example 6.
39.
(-3)/
40. Σ(-2)'
41. 48 (¹)
1=1
42.
· 243 (²)
43. 24
45. Concept Check Under what conditions does the sum of an infinite geometric series
exist?
46. The number 0.999... can be written as the sum of the terms of an infinite geometric
sequence: 0.9 + 0.09 +0.009+. Here we have a₁ = 0.9 and r= 0.1. Use the
formula for So, to find this sum. Does intuition indicate that this answer is correct?
Find r for each infinite geometric sequence. Identify any whose sum diverges.
47. 12, 24, 48, 96,...
48. 2,-10, 50, -250, ...
X-S
49. -48, -24, -12, -6, ...
50. 625, 125, 25, 5,...
Work each problem. See Examples 7 and 8.
S
51. Use lim S, to show that 2+1+ +
++
converges to 4.
818
52. We determined that 1 ++ 1 1
+
+
27
converges to using an argument
limits. Use the formula for the sum of the terms of an infinito
obtain the same result
ܐ܂
44.
9

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