Math 112 Quiz Solutions: Sigma, Infinite Series, Sequences - Prof. Garrett Alston, Quizzes of Algebra

Download Math 112 Quiz Solutions: Sigma, Infinite Series, Sequences - Prof. Garrett Alston and more Quizzes Algebra in PDF only on Docsity! Math 112 Quiz Problem 1 (3 points): Write the following sum in sigma notation: 4 + 1 + 1 4 + 1 16 + 1 64 Solution: 5∑ k=1 4( 1 4 )k Problem 2 (2 points): Find the sum of the infinite geometric series: 1 + 1 3 + 1 9 + 1 27 + ... Solution: 1 1 − 1 3 = 3 2 Problem 3 (3 points): Suppose that the 4th term of an arithmetic sequence is 10 and the 7th term is 25. Find the 8th term. Solution: a4 = 10 and a7 = 25, so d = (25 − 10)/(7 − 4) = 5. So a8 = 25 + 5 = 30 Problem 4 (2 points): Suppose that a geometric sequence has a1 = 1 and the common ratio is -2. Find a4. Solution: an = 1(−2) n−1, so a4 = (−2) 3 = −8.