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:

Manoj and Shira were asked to find an explicit formula for the sequence -9,-27,-81,-243,dots, where the first term should be h(1). Manoj said the formula is h(n)=-9*3^(n), and Shira said the formula is h(n)=-3*3^(n). Which one of them is right? Choose 1 answer: (A) Only Manoj (B) Only Shira (c) Both Manoj and Shira (D) Neither Manoj nor Shira

Manoj and Shira were asked to find an explicit formula for the sequence \newline−9,−27,−81,−243,…-9,-27,-81,-243,\dots, where the first term should be \newlineh(1)h(1).\newlineManoj said the formula is \newlineh(n)=−9⋅3(n−1)h(n)=-9\cdot3^{(n-1)}, and\newlineShira said the formula is \newlineh(n)=−3⋅3(n−1)h(n)=-3\cdot3^{(n-1)}.\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Manoj\newline(B) Only Shira\newline(C) Both Manoj and Shira\newline(D) Neither Manoj nor Shira

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. Manoj and Shira were asked to find an explicit formula for the sequence \newline−9,−27,−81,−243,…-9,-27,-81,-243,\dots, where the first term should be \newlineh(1)h(1).\newlineManoj said the formula is \newlineh(n)=−9⋅3(n−1)h(n)=-9\cdot3^{(n-1)}, and\newlineShira said the formula is \newlineh(n)=−3⋅3(n−1)h(n)=-3\cdot3^{(n-1)}.\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Manoj\newline(B) Only Shira\newline(C) Both Manoj and Shira\newline(D) Neither Manoj nor Shira
  1. Identifying Geometric Sequence: The sequence given is −9,−27,−81,−243,…-9, -27, -81, -243, \ldots which is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio.
  2. Finding the Common Ratio: To find the common ratio rr, we divide the second term by the first term: r=−27−9=3r = \frac{-27}{-9} = 3.
  3. Writing the Explicit Formula: The first term of the sequence is h(1)=−9h(1) = -9. Using the common ratio r=3r = 3, we can write the explicit formula for the nnth term as h(n)=h(1)⋅r(n−1)h(n) = h(1) \cdot r^{(n-1)}.
  4. Checking Manoj's Formula: Substituting the values of h(1)h(1) and rr into the formula, we get h(n)=−9×3(n−1)h(n) = -9 \times 3^{(n-1)}.
  5. Checking Shira's Formula: Now let's check Manoj's formula: h(n)=−9×3nh(n) = -9 \times 3^n. This formula would give us the sequence −9-9, −27-27, −81-81, −243-243, ... if we start counting from n=0n = 0. However, we are asked to start from n=1n = 1, so Manoj's formula is incorrect for this sequence.
  6. Determining the Correct Answer: Let's check Shira's formula: h(n)=−3⋅3nh(n) = -3 \cdot 3^n. If we substitute n=1n = 1, we get h(1)=−3⋅31=−9h(1) = -3 \cdot 3^1 = -9, which is the correct first term. However, for n=2n = 2, we get h(2)=−3⋅32=−27h(2) = -3 \cdot 3^2 = -27, which is also the correct second term. But the formula should be h(n)=−3⋅3(n−1)h(n) = -3 \cdot 3^{(n-1)} to match the sequence starting from n=1n = 1. Therefore, Shira's formula is also incorrect.
  7. Determining the Correct Answer: Let's check Shira's formula: h(n)=−3⋅3nh(n) = -3 \cdot 3^n. If we substitute n=1n = 1, we get h(1)=−3⋅31=−9h(1) = -3 \cdot 3^1 = -9, which is the correct first term. However, for n=2n = 2, we get h(2)=−3⋅32=−27h(2) = -3 \cdot 3^2 = -27, which is also the correct second term. But the formula should be h(n)=−3⋅3(n−1)h(n) = -3 \cdot 3^{(n-1)} to match the sequence starting from n=1n = 1. Therefore, Shira's formula is also incorrect.Since neither Manoj's nor Shira's formula correctly represents the sequence when starting from n=1n = 1, the correct answer is (D) Neither Manoj nor Shira.

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