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:

{[a(1)=20],[a(n)=a(n-1)*(3)/(2)]:} What is the 3^("rd ") term in the sequence?

{a(1)=20a(n)=a(n−1)⋅32 \left\{\begin{array}{l} a(1)=20 \\ a(n)=a(n-1) \cdot \frac{3}{2} \end{array}\right. \newlineWhat is the 3rd  3^{\text {rd }} term in the sequence?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Geometric sequencesright chevron icon

Full solution

Q. {a(1)=20a(n)=a(n−1)⋅32 \left\{\begin{array}{l} a(1)=20 \\ a(n)=a(n-1) \cdot \frac{3}{2} \end{array}\right. \newlineWhat is the 3rd  3^{\text {rd }} term in the sequence?
  1. Define Recursive Sequence: The sequence is defined recursively, with the first term a(1)a(1) given as 2020. The nnth term a(n)a(n) is defined in terms of the previous term a(n−1)a(n-1) as a(n)=a(n−1)×(32)a(n) = a(n-1) \times (\frac{3}{2}). To find the third term a(3)a(3), we need to find the second term a(2)a(2) first, using the first term a(1)a(1). a(2)=a(1)×(32)=20×(32)=30a(2) = a(1) \times (\frac{3}{2}) = 20 \times (\frac{3}{2}) = 30.
  2. Calculate Second Term: Now that we have the second term a(2)a(2), we can find the third term a(3)a(3) by applying the recursive formula again.a(3)=a(2)×(32)=30×(32)=45.a(3) = a(2) \times \left(\frac{3}{2}\right) = 30 \times \left(\frac{3}{2}\right) = 45.

More problems from Geometric sequences

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 6 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 6 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 2 months ago

View all (131)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant