meredith48034
Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Write an explicit and a cursive equation for the geometric sequence

a. 2, 10, 50, 250, 1250, . . .

Sagot :

jcherry99

Answer:

Step-by-step explanation:

Explicit

a_n = a1 * r^(n - 1)

Find r by dividing term (n)/(n - 1)

r = 250 / 50

r = 5

a_n = a * r^(n - 1)

Recursive

a_n = a_(n-1)*r

Try an example

Find a_6

a_6 = 2 * 5^(6 - 1)

a_6 = 2 * 5^5

a_6 = 2 * 3125

a_6 = 6250

recursive

a_n = a_(n - 1)*r

r = 5

n = 6

a_n = 1250 * 5

a_n = 6250

The explicit method looks a whole lot easier, but not for a machine made by Dell and programed by Microsoft. A computer doesn't really mind doing a whole lot of calculations that are repetitive. And in many cases recursive is easier to program and is faster.

sqdancefan

Answer:

  • explicit: a(n) = 2·5^(n-1)
  • recursive: a(1) = 2; a(n) = a(n-1)×5

Step-by-step explanation:

The given sequence is exponential with a first term of a1 = 2 and a common ratio of r = 10/2 = 5.

The explicit equation for an exponential sequence is ...

  a(n) = a(1)×r^(n -1)

So, for the given parameters, the explicit equation is ...

  a(n) = 2×5^(n -1)

__

The recursive equation for any series defines the next term as a function of previous terms. For a geometric sequence the next term is the previous term multiplied by the common ratio. For this sequence, the recursive definition is ...

  a(1) = 2

  a(n) = 5×a(n-1)

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.