Math Review: Arithmetic, Geometric Sequences, Induction, Binomial Coefficients, Study notes of Algebra

Download Math Review: Arithmetic, Geometric Sequences, Induction, Binomial Coefficients and more Study notes Algebra in PDF only on Docsity! 1 Math 1521 AS ( College Algebra ),WEB Some Review Problems Sheet #4 Topics: 17.1,17.2 1.a.Find the 13th term of the Arithmetic sequence : 2,6,10,14,18……………… b. Find the 9th term of the Geometric sequence: 2, ..........,......... 27 2, 9 2, 3 2 2. For the Arithmetic sequence .............,.........3,8,13,18 a. Find the common Difference d. b. Find the twenty-fourth term, 24a c. Find the sum, of the first 36 terms. ,36S 3. Find the first term, and the common difference, d, of the Arithmetic sequence whose sum of the first 12 terms, is 246 and whose twelfth term , is 37. ,1a ,12S 12a 4. For the Geometric sequence 49,7,1,………………………………. i. Find the common ratio, r. ii. Find the sixth term, 6a iii. Find the sum, of the first eight terms 8S iv. Find the infinite sum, if it exists. ∞S 2 5. Consider the statement ( )( ) ( )164 3 11212....................5.33.1: 2 −+=+−+++ nnnnnSn a. Write the statement kS b. Write the statement 2+kS 6. Use the Mathematical induction to prove that the statement ( ) ( )3214............1395: +=+++++ nnnSn holds true for all positive integers n. 7. Given the statement ( )1 2 ......................4321: +=+++++ nnnSn a. Write the statement 1S b. Write the statement kS c. Write the statement 1+kS