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:

Find an explicit formula for the geometric sequence −1,−7,−49,−343-1, -7, -49, -343 the first term should be b(1)b(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. Find an explicit formula for the geometric sequence −1,−7,−49,−343-1, -7, -49, -343 the first term should be b(1)b(1)
  1. Identify Sequence Type: Identify the type of sequence.\newlineThe sequence −1-1, −7-7, −49-49, −343-343, ... appears to be geometric because each term is obtained by multiplying the previous term by a common ratio.
  2. Find First Term and Ratio: Determine the first term b(1)b(1) and the common ratio rr of the sequence.\newlineFirst term: b(1)=−1b(1) = -1\newlineTo find the common ratio, divide the second term by the first term: r=−7−1=7r = \frac{-7}{-1} = 7
  3. Formulate Explicit Formula: Formulate the explicit formula for the geometric sequence using b(1)b(1) and rr. The general formula for the nnth term of a geometric sequence is b(n)=b(1)⋅r(n−1)b(n) = b(1) \cdot r^{(n - 1)}. Substitute −1-1 for b(1)b(1) and 77 for rr to get the explicit formula. b(n)=−1⋅7(n−1)b(n) = -1 \cdot 7^{(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