The nth term of a sequence is given.an = 4(−0.5)n − 1(a) Find the first five terms of the sequence.a1 = a2 = a3 = a4 = a5 = (b) What is the common ratio r?
Question
The nth term of a sequence is given.an = 4(−0.5)n − 1(a) Find the first five terms of the sequence.a1 = a2 = a3 = a4 = a5 = (b) What is the common ratio r?
Solution
(a) To find the first five terms of the sequence, we substitute the values n = 1, 2, 3, 4, and 5 into the formula an = 4(-0.5)n - 1.
a1 = 4(-0.5)¹ - 1 = -2 a2 = 4(-0.5)² - 1 = 1 a3 = 4(-0.5)³ - 1 = -2.5 a4 = 4(-0.5)⁴ - 1 = 1.5 a5 = 4(-0.5)⁵ - 1 = -2.75
(b) The common ratio r of a geometric sequence is the ratio of any term to the previous term. In this case, we can find r by dividing a2 by a1, or a3 by a2, and so on.
r = a2 / a1 = 1 / -2 = -0.5
So, the common ratio r is -0.5.
Similar Questions
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 4(3)n
Determine the common ratio r, the fifth term, and the nth term of the geometric sequence.7, 145, 2825, 56125, . . .r = a5 = an =
Find the nth term of the geometric sequence with given first term a and common ratio r.a = −6, r = −3an = What is the fourth term?a4 =
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 69n − 25
1. 1. Find these terms of the sequence {an}, where an = 2 (−3)n + 5n.a) a0 b) a1 c) a4 d) a5
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.