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Exercise 1. Find the general term of a sequence whose the first four terms are: a. 3,6,9, 12, -.. b. 1,-2,4,-8, ... Exercise 2. Write the given alternating series using the summation notation with the summing index n starting at 1. 1 1 1- 1- 27 81 Exercise 3. Determine whether the given sequence can be the first four term of an arithmetic sequence or geometric sequence. a. 8,2,0.5,0.125,... b. -7,-2,3,8, . c. 1,5, 25, 100, ..

Exercise 1. Find the general term of a sequence whose the first four terms are: a. 3,6,9, 12, -.. b. 1,-2,4,-8, ... Exercise 2. Write the given alternating series using the summation notation with the summing index n starting at 1. 1 1 1- 1- 27 81 Exercise 3. Determine whether the given sequence can be the first four term of an arithmetic sequence or geometric sequence. a. 8,2,0.5,0.125,... b. -7,-2,3,8, . c. 1,5, 25, 100, ..

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise 1. Find the general term of a sequence whose the first four terms are: a. 3,6,9, 12, -.. b. 1,-2,4,-8, ... Exercise 2. Write the given alternating series using the summation notation with the summing index n starting at 1. 1. 1 + 9. 1 1 1- 27 81 Exercise 3. Determine whether the given sequence can be the first four term of an arithmetic sequence or geometric sequence. a. 8,2,0.5,0.125,... b. -7,-2,3,8, c. 1,5,25, 100,-.. Exercise 4. If the 1st and 15th terms an arithmetic sequence are -5 and 23, respectively, find the 73rd term of the sequence. Exercise 5. Find the sum of all even numbers between 24 and 208. Exercise 6. Find the sum of the first eight terms in the geometric sequence: 100, 100(1.08), 100(1.08²), -… Exercise 7. A person borrows $6000 and agrees to repay the loan in monthly installments over 5 years. The agreement is to pay 1% of the unpaid balance each month for using the money and $100 each month to reduce the loan. What is the total cost of the loan over 5 years?
Transcribed Image Text:Exercise 1. Find the general term of a sequence whose the first four terms are: a. 3,6,9, 12, -.. b. 1,-2,4,-8, ... Exercise 2. Write the given alternating series using the summation notation with the summing index n starting at 1. 1. 1 + 9. 1 1 1- 27 81 Exercise 3. Determine whether the given sequence can be the first four term of an arithmetic sequence or geometric sequence. a. 8,2,0.5,0.125,... b. -7,-2,3,8, c. 1,5,25, 100,-.. Exercise 4. If the 1st and 15th terms an arithmetic sequence are -5 and 23, respectively, find the 73rd term of the sequence. Exercise 5. Find the sum of all even numbers between 24 and 208. Exercise 6. Find the sum of the first eight terms in the geometric sequence: 100, 100(1.08), 100(1.08²), -… Exercise 7. A person borrows $6000 and agrees to repay the loan in monthly installments over 5 years. The agreement is to pay 1% of the unpaid balance each month for using the money and $100 each month to reduce the loan. What is the total cost of the loan over 5 years?
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