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 explicit formula that represents the sequence defined by the following recursive formula: a_(1)=5" and "a_(n)=a_(n-1)+3 Answer: a_(n)=

Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=5 and an=an−1+3 a_{1}=5 \text { and } a_{n}=a_{n-1}+3 \newlineAnswer: an= a_{n}=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Identify a sequence as explicit or recursiveright chevron icon

Full solution

Q. Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=5 and an=an−1+3 a_{1}=5 \text { and } a_{n}=a_{n-1}+3 \newlineAnswer: an= a_{n}=
  1. Identify First Term: Identify the first term of the sequence.\newlineThe first term is given as a1=5a_{1}=5.
  2. Determine Common Difference: Determine the common difference in the recursive formula.\newlineThe recursive formula an=an−1+3a_{n}=a_{n-1}+3 suggests that each term is 33 more than the previous term. This indicates a common difference of 33.
  3. Write Explicit Formula: Write the explicit formula based on the first term and the common difference.\newlineThe explicit formula for an arithmetic sequence is given by an=a1+(n−1)da_{n}=a_{1}+(n-1)d, where a1a_{1} is the first term and dd is the common difference.
  4. Substitute Known Values: Substitute the known values into the explicit formula.\newlineSubstituting a1=5a_{1}=5 and d=3d=3 into the formula, we get an=5+(n−1)⋅3a_{n}=5+(n-1)\cdot 3.
  5. Simplify Formula: Simplify the explicit formula.\newlineSimplifying the formula, we get an=5+3n−3a_{n}=5+3n-3.\newlineCombining like terms, we get an=3n+2a_{n}=3n+2.

More problems from Identify a sequence as explicit or recursive

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 (73)

Related topics

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