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:

In an arithmetic sequence, the first term, a_(1), is equal to 3 , and the fourth term, a_(4), is equal to 24 . Which number represents the common difference of the arithmetic sequence? d=4 d=5 d=6 d=7

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 33 , and the fourth term, a4 a_{4} , is equal to 2424 . Which number represents the common difference of the arithmetic sequence?\newlined=4 d=4 \newlined=5 d=5 \newlined=6 d=6 \newlined=7 d=7

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Convert a recursive formula to an explicit formularight chevron icon

Full solution

Q. In an arithmetic sequence, the first term, a1 a_{1} , is equal to 33 , and the fourth term, a4 a_{4} , is equal to 2424 . Which number represents the common difference of the arithmetic sequence?\newlined=4 d=4 \newlined=5 d=5 \newlined=6 d=6 \newlined=7 d=7
  1. Given terms: We are given the first term of the arithmetic sequence a1a_{1} is 33 and the fourth term a4a_{4} is 2424. The common difference dd can be found by using the formula for the nth term of an arithmetic sequence, which is an=a1+(n−1)da_{n} = a_{1} + (n - 1)d. We can set up the equation for the fourth term.
  2. Set up equation: Substitute the known values into the formula to find the common difference. We have a4=24a_{4} = 24, a1=3a_{1} = 3, and n=4n = 4. So, 24=3+(4−1)d24 = 3 + (4 - 1)d.
  3. Simplify equation: Simplify the equation: 24=3+3d24 = 3 + 3d. Subtract 33 from both sides to isolate the term with dd: 24−3=3d24 - 3 = 3d.
  4. Isolate term: Perform the subtraction: 21=3d21 = 3d. Now, divide both sides by 33 to solve for dd: 21÷3=d21 \div 3 = d.
  5. Calculate common difference: Calculate the division: 7=d7 = d. So, the common difference of the arithmetic sequence is 77.

More problems from Convert a recursive formula to an explicit formula

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 (5)

Related topics

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