University:
Carleton College
Course:
MATH 111 | Introduction to Calculus
Academic year:

2024
Views:

355

Pages:

2
Author:

SpaceCadet101

Name__________________________Date_________________Hour________ Honors Pre-calculus 8.1-8.3 Review/Sequences and Series In #1-4, state whether each type of sequence is Arithmetic, Geometric, or Neither and find an explicit formula an. Calculators will be allowed on the entire test! 1. 17, 13, 9, 5, ... 2. AGN an=_________________ 4. AGN 3.  1, AGN an=_________________ 1 1 1 , , ,... 4 16 64 AGN an=_________________ 3, 18, 108, 648, ... an=_________________ 5. In an arithmetic sequence, a4  11 and a8  39. Find a17 a17=__________________ 7. 1 4 9 16 , , ,... 3 5 7 9 6. In an geometric sequence, a4  12 and a7  96. Find a14 a14=__________________ Give a recursive definition for the following sequence 8. 2, -4, 8, -16,…….. 3, 6, 12, 24,…….. an+1=__________________ 9. 0.25 + 0.5 + 1 + 2 +… Find S15=____________________ an+1=__________________ Find the following sums 10. 2 + 6 + 10 + 14……+ 398 + 402 Sn=____________________ Name__________________________Date_________________Hour________ 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, etc….If this pattern continues, how many kernels would be placed on the last square? On the whole board? 12. Each year Jimmy invests $1,950 per year ($75 per pay check) into his retirement account, which on average earns 9% interest per year. After 40 years of work, how much money does he have in his account? (after the first year $1950 is deposited, a year later that earns 9% and another $1950 is added) 13. Find the sum of:  n 17 3 14. Find the sum of:   2 3   n 0  7  1 1 ___________________ n __________________ 15. Express the following series using sigma notation, then find the sum. 1 3 7 31    ...  4 8 16 64  1. arith.; a n  4n  21 2. neither; a  n =__________________ n2 2n  1 3. geom..; 7. a1  2; a n 1  2a n 6. -12288 10. 20402 11. last square = 2 63 ; whole board =  1  2 64 12. $718,169.14 13. 23392  5 n 1 4. geom.; an  36n1 8. a1  3; a n 1  2a n 5. 102 14. 4.2 or 21  1 an  1    4  or 1.844674407 x 1019 15. 2  1 ; 129 n 2 n 1 64 9. 8191.75