Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Complete the recursive formula of the geometric sequence {:[16","3.2","0.64","0.128","dots.],[a(1)=],[a(n)=a(n-1)*]:}

Complete the recursive formula of the geometric sequence\newline16,3.2,0.64,0.128,….  16,3.2,0.64,0.128, \ldots \text {. } \newlinea(1)=□ a(1)= \square \newlinea(n)=a(n−1)⋅□ a(n)=a(n-1) \cdot \square

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write variable expressions for geometric sequencesright chevron icon

Full solution

Q. Complete the recursive formula of the geometric sequence\newline16,3.2,0.64,0.128,….  16,3.2,0.64,0.128, \ldots \text {. } \newlinea(1)=□ a(1)= \square \newlinea(n)=a(n−1)⋅□ a(n)=a(n-1) \cdot \square
  1. Given Sequence: We are given the geometric sequence: 16,3.2,0.64,0.128,…16, 3.2, 0.64, 0.128, \ldots\newlineTo find the recursive formula, we need to determine the common ratio by dividing any term by the previous term.\newlineLet's divide the second term by the first term to find the common ratio (r)(r).\newliner=3.216r = \frac{3.2}{16}
  2. Find Common Ratio: Now, let's perform the calculation to find the value of rr.r=3.216=0.2r = \frac{3.2}{16} = 0.2This means that each term is multiplied by 0.20.2 to get the next term.
  3. Calculate Common Ratio: We are also given the first term of the sequence, which is a(1)=16a(1) = 16. Now we can write the recursive formula for the sequence using the common ratio and the first term. The recursive formula is: a(n)=a(n−1)×ra(n) = a(n-1) \times r Substitute the value of rr into the formula. a(n)=a(n−1)×0.2a(n) = a(n-1) \times 0.2

More problems from Write variable expressions for geometric sequences

Question
What is the period of\newliney=−2sin⁡(23x−4)? y=-2 \sin \left(\frac{2}{3} x-4\right) ? \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the period of\newliney=8cos⁡(5πx+3π2)−9? y=8 \cos \left(5 \pi x+\frac{3 \pi}{2}\right)-9 ? \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
z=91−27i z=91-27 i \newlineWhat is the real part of z z ?\newlineWhat is the imaginary part of z z ?
Get tutor helpright-arrow

Posted 3 months ago

Question
z=−19i+14 z=-19 i+14 \newlineWhat is the real part of z z ?\newlineWhat is the imaginary part of z z ?
Get tutor helpright-arrow

Posted 3 months ago

Question
z=−302+19.3i z=-302+19.3 i \newlineWhat is the real part of z z ?\newlineWhat is the imaginary part of z z ?
Get tutor helpright-arrow

Posted 3 months ago

Question
The sum of the first 33 terms of a geometric series is 171171 and the common ratio is 23 \frac{2}{3} .\newlineWhat is the first term of the series?
Get tutor helpright-arrow

Posted 3 months ago

Question
The first term in a geometric series is 55 and the common ratio is 22 .\newlineFind the sum of the first 1010 terms in the series.
Get tutor helpright-arrow

Posted 3 months ago

Question
What happens to the value of the expression 70−3g 70-3 g as g g increases?\newlineChoose 11 answer:\newline(A) It increases.\newline(B) It decreases.\newline(C) It stays the same.
Get tutor helpright-arrow

Posted 3 months ago

Question
What happens to the value of the expression m−10 m-10 as m m decreases?\newlineChoose 11 answer:\newline(A) It increases.\newline(B) It decreases.\newline(C) It stays the same.
Get tutor helpright-arrow

Posted 3 months ago

Question
What happens to the value of the expression 20+a 20+a as a a increases?\newlineChoose 11 answer:\newline(A) It increases.\newline(B) It decreases.\newline(C) It stays the same.
Get tutor helpright-arrow

Posted 3 months ago

View all (22)