University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2024
Views:

117

Pages:

3
Author:

Giselle A.

HPC Sequences & Series Quiz 8.1-8.3 Review Name: State whether each type of sequence is arithmetic, geometric, or neither, and find an explicit formula 𝒂𝒏 . 1. 17, 13, 9, 5, … 1. A G N 𝑎𝑛 = _________________________ 2. 1 4 9 16 , , , ,… 3 5 7 9 2. A G N 𝑎𝑛 = _________________________ 3. −1, 1 , 4 1 − 16 , 1 ,… 64 3. A G N 𝑎𝑛 = _________________________ 4. 3, 18, 108, 648, … 4. A G N 𝑎𝑛 = _________________________ 5. In an arithmetic sequence, 𝑎4 = 11 and 𝑎8 = 39. Find 𝑎17 . 5.)________________________ 6. In an geometric sequence, 𝑎4 = −12 and 𝑎7 = 96. Find 𝑎14 . 6.)________________________ Give a recursive definition for the following sequences. Don’t forget to state the first term! The formula means NOTHING without it! 7. 2, −4, 8, −16, … 8. 3, 6, 12, 24, … 7.)________________________ __________________________ 8.)________________________ __________________________ Find the following sums. 9. 0.25 + 0.5 + 1 + 2 + ⋯ 𝑛 = 15 10. 2 + 6 + 10 + 14 + ⋯ + 398 + 402 9.)________________________ 10.)_______________________ 11. On an 8 x 8 checker board, if you placed a kernel of corn on the first square, two kernels on the second, four on the third, eight on the fourth and so on, how many kernels would be placed in the last square if this pattern continued? How many would be placed on the whole board? 11.)_______________________ 12. At the beginning of each year Jimmy invests $1950 per year into his retirement account. On the average, the account earns 9% interest per year. After 40 years of work, how much money does he have in his account? 12.)_______________________ Find the following sums. 13. 17 ∑ (𝑛3 𝑛=1 − 1) 14. ∞ 2 𝑛 ∑ 3( ) 7 13.)_______________________ 𝑛=0 14.)_______________________ 15. Express the following series using sigma notation, then find the sum. 1 4 + 3 8 + 7 16 31 64 + ⋯+ 15.)_______________________ __________________________ 16. Find the sum of the first 100 positive multiples of 5. 16.)_______________________ 8 17. Find the sum 1 𝑛−1 ∑ 24 ( ) 6 17.)_______________________ 𝑛=1 18. 4 5−2+5− Find the sum: 8 16 + 125 − 25 ⋯ 18.)_______________________ 7 19. Find the sum ∑ (8𝑛 − 5) 19.)_______________________ 𝑛=1 7 20. Find the sum ∑ 8𝑛 − 5 20.)_______________________ 𝑛=1 Answers 1 𝑛−1 4 𝑛2 2𝑛 + 1 1. Arithmetic; 𝑎𝑛 = −4𝑛 + 21 2. Neither; 𝑎𝑛 = 4. Geometric; 𝑎𝑛 = 3(6)𝑛−1 5. 102 6. −12,288 8. 𝑎1 = 3; 𝑎𝑛+1 = 2𝑎𝑛 9. 8,191.75 10. 20,402 11. Last Square: 263 3. Geometric; 𝑎𝑛 = −1 (− ) 7. 𝑎1 = 2; 𝑎𝑛+1 = −2𝑎𝑛 Whole Board: −(1 − 264 ) or 1.844674407 𝑥 1019 13. 23,392 14. 4.2 or 17. 28.80 18. 25 7 21 5 15. 2𝑛 − 1 129 ; 64 2𝑛 + 1 19. 189 12. $718,169.14 16. 25,250 20. 219