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:

Write an equation to describe the sequence below. Use n n to represent the position of a term in the sequence, where n=1 n = 1 for the first term.\newline9,18,36,… 9 , 18 , 36 , \ldots \newlineWrite your answer using decimals and integers.\newlinean= a_n = _____(_____)n−1^{n - 1}

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. Write an equation to describe the sequence below. Use n n to represent the position of a term in the sequence, where n=1 n = 1 for the first term.\newline9,18,36,… 9 , 18 , 36 , \ldots \newlineWrite your answer using decimals and integers.\newlinean= a_n = _____(_____)n−1^{n - 1}
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence is 9,18,36,…9, 18, 36, \ldots where each term appears to be twice the previous term. This suggests that the sequence is geometric.
  2. Determine first term and ratio: Determine the first term (a1a_1) and the common ratio (rr).\newlineThe first term a1a_1 is the first number in the sequence, which is 99.\newlineTo find the common ratio rr, we divide the second term by the first term: r=189=2r = \frac{18}{9} = 2.
  3. Write nth term formula: Write the formula for the nth term of a geometric sequence.\newlineThe nth term ana_n of a geometric sequence is given by the formula an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n - 1)}.
  4. Substitute values into formula: Substitute the values of a1a_1 and rr into the formula.\newlineWe have a1=9a_1 = 9 and r=2r = 2, so the formula becomes an=9×2(n−1)a_n = 9 \times 2^{(n - 1)}.

More problems from Write variable expressions for 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 (52)

Related topics

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