Technical Mathematics, Sixth Edition

20.6. CHAPTER 20 REVIEW PROBLEMS

1. Find the sum of seven terms of the AP: −4, −1, 2, ... 35

2. Find the tenth term of (1 − y)¹⁴. −2002y⁹

3. Insert four arithmetic means between 3 and 18. 6, 9, 12, 15

4. How many terms of the AP −5, −2, 1, ... will give a sum of 63? 9

5. Insert four harmonic means between 2 and 12. , 3, 4, 6

6. Find the twelfth term of an AP with first term 7 and common difference 5. 62

7. Find the sum of the first 10 terms of the AP 1, , ... 85

Expand each binomial.

1. 

2. (a − 2)⁵ a⁵ − 10a⁴ + 40a³ − 80a² + 80a − 32

3. (x − y³)⁷ x⁷ − 7x⁶y³ + 21x⁵y⁶ − 35x⁴y⁹ + 35x³y¹² − 21x²y¹⁵ + 7xy¹⁸ − y²¹

4. Find the fifth term of a GP with first term 3 and common ratio 2. 48

5. Find the fourth term of a GP with first term 8 and common ratio −4. −512

Evaluate each limit.

Find the sum of infinitely many terms of each GP.

1. 4, 2, 1, ... 8

2. 

3. Find the seventh term of the harmonic progression 3, , 4, ... 12

4. Find the sixth term of a GP with ...