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 the 14 th term of the arithmetic sequence -5x+1,-12 x-3,-19 x-7,dots Answer:

Find the 1414 th term of the arithmetic sequence −5x+1,−12x−3,−19x−7,… -5 x+1,-12 x-3,-19 x-7, \ldots \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Evaluate variable expressions for Sequencesright chevron icon

Full solution

Q. Find the 1414 th term of the arithmetic sequence −5x+1,−12x−3,−19x−7,… -5 x+1,-12 x-3,-19 x-7, \ldots \newlineAnswer:
  1. Find Common Difference: To find the 14th14^{\text{th}} term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the nthn^{\text{th}} term of an arithmetic sequence, which is an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nthn^{\text{th}} term, a1a_1 is the first term, nn is the term number, and dd is the common difference.\newlineFirst, let's find the common difference (d)(d) by subtracting the first term from the second term.\newlined=(−12x−3)−(−5x+1)d = (-12x - 3) - (-5x + 1)\newlinenthn^{\text{th}}00\newlinenthn^{\text{th}}11
  2. Calculate 1414th Term: Now that we have the common difference, we can use the formula to find the 1414th term a14a_{14}.a14=a1+(14−1)(−7x−4)a_{14} = a_1 + (14 - 1)(-7x - 4)a14=(−5x+1)+13(−7x−4)a_{14} = (-5x + 1) + 13(-7x - 4)
  3. Simplify Expression: Next, we will simplify the expression to find a14a_{14}. \newlinea14=(−5x+1)+(−91x−52)a_{14} = (-5x + 1) + (-91x - 52)\newlinea14=−5x+1−91x−52a_{14} = -5x + 1 - 91x - 52\newlinea14=−96x−51a_{14} = -96x - 51

More problems from Evaluate variable expressions for 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 (72)

Related topics

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