A sequence {a_n}, n = 1, 2, 3, ... is defined recursively by a_1 = 1/2,anda_n = 7a_(n–1), n > 1.Then, an expression for a_n isQuestion 6Answera.(7/2)^(n-1)b.(7^(n-1))/2c.None of the Given Choicesd.7/(2^(n-1))e.(2^(n-1))/7
Question
A sequence {a_n}, n = 1, 2, 3, ... is defined recursively by a_1 = 1/2,anda_n = 7a_(n–1), n > 1.Then, an expression for a_n isQuestion 6Answera.(7/2)^(n-1)b.(7^(n-1))/2c.None of the Given Choicesd.7/(2^(n-1))e.(2^(n-1))/7
Solution
The given sequence is a geometric sequence where each term is 7 times the previous term. The first term a_1 is 1/2 and the common ratio is 7.
In a geometric sequence, the nth term a_n can be found using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.
Substituting the given values into the formula, we get a_n = (1/2) * 7^(n-1).
Therefore, the expression for a_n is (7^(n-1))/2, which corresponds to option b.
Similar Questions
Findthe7thtermofthesequencedescribedbelow,wherenrepresentsthepositionofaterminthesequence.an = 13(2)n − 1Write your answer as a decimal or integer.a7 = Submit
Write an equation for the nth term of the geometric sequence $7,\ 28,\ 112,\ 448,\ ...$7, 28, 112, 448, ... . Then find $a_6$a6 .An equation for the nth term of the geometric sequence is $a_n=$an= $\text{(}$( $\text{)}$) $^{n-1}$n−1 .$a_6=$a6=
Q 63. In the case where n' is a positive integer and limx—> 7(x^n-7^n)/(x-7) = 147, then n is equals Ops: A. n=3 B. n=1 C. n=2 D. n=4
2. What is the term a8 of the sequence {an} if an equalsa) 2n−1? b) 7? c) 1 + (−1)n? d) −(−2)n?
Instructions: Given one form of a sequence, write the other form. Recursivean=an−1⋅−3𝑎𝑛=𝑎𝑛−1⋅−3a1=2𝑎1=2Explicit Forman=𝑎𝑛= Answer 1 Question 7 (( Answer 2 Question 7 )n−1
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.