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:

{[b(1)=15],[b(n)=b(n-1)*(-3)]:} What is the 4^("th ") term in the sequence?

{b(1)=15b(n)=b(n−1)⋅(−3) \left\{\begin{array}{l} b(1)=15 \\ b(n)=b(n-1) \cdot(-3) \end{array}\right. \newlineWhat is the 4th  4^{\text {th }} 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. {b(1)=15b(n)=b(n−1)⋅(−3) \left\{\begin{array}{l} b(1)=15 \\ b(n)=b(n-1) \cdot(-3) \end{array}\right. \newlineWhat is the 4th  4^{\text {th }} term in the sequence?
  1. Given information: We are given the first term of the sequence, b(1)=15b(1) = 15, and a recursive formula for the sequence, b(n)=b(n−1)×(−3)b(n) = b(n-1) \times (-3). To find the 44th term, we need to apply the recursive formula three times starting from the first term.
  2. Find second term: First, we find the second term using the recursive formula. The second term is b(2)=b(1)×(−3)b(2) = b(1) \times (-3).\newlineCalculation: b(2)=15×(−3)=−45b(2) = 15 \times (-3) = -45.
  3. Find third term: Next, we find the third term using the recursive formula. The third term is b(3)=b(2)×(−3)b(3) = b(2) \times (-3).\newlineCalculation: b(3)=−45×(−3)=135b(3) = -45 \times (-3) = 135.
  4. Find fourth term: Finally, we find the fourth term using the recursive formula. The fourth term is b(4)=b(3)×(−3)b(4) = b(3) \times (-3).\newlineCalculation: b(4)=135×(−3)=−405b(4) = 135 \times (-3) = -405.

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 9 months ago

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

Posted 5 months ago

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

Posted 5 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 5 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 7 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 5 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 7 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 7 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 9 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 5 months ago

View all (116)

Related topics

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