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:

{[b(1)=-7],[b(n)=b(n-1)+12]:} Find the 4^("th ") term in the sequence.

{b(1)=−7b(n)=b(n−1)+12 \left\{\begin{array}{l} b(1)=-7 \\ b(n)=b(n-1)+12 \end{array}\right. \newlineFind the 4th  4^{\text {th }} term in the sequence.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Arithmetic sequencesright chevron icon

Full solution

Q. {b(1)=−7b(n)=b(n−1)+12 \left\{\begin{array}{l} b(1)=-7 \\ b(n)=b(n-1)+12 \end{array}\right. \newlineFind the 4th  4^{\text {th }} term in the sequence.
  1. Understand the sequence definition: Understand the sequence definition.\newlineThe sequence is defined recursively, with the first term b(1)b(1) given as −7-7. Each subsequent term is found by adding 1212 to the previous term. This means that to find the 44th term, we need to apply the recursive formula three times starting from the first term.
  2. Find the second term: Find the second term using the recursive formula.\newlineWe know that b(1)=−7b(1) = -7. To find b(2)b(2), we use the formula b(n)=b(n−1)+12b(n) = b(n-1) + 12.\newlineb(2)=b(1)+12=−7+12=5b(2) = b(1) + 12 = -7 + 12 = 5.
  3. Find the third term: Find the third term using the recursive formula.\newlineNow that we have b(2)b(2), we can find b(3)b(3) by adding 1212 to b(2)b(2).\newlineb(3)=b(2)+12=5+12=17b(3) = b(2) + 12 = 5 + 12 = 17.
  4. Find the fourth term: Find the fourth term using the recursive formula.\newlineFinally, we find b(4)b(4) by adding 1212 to b(3)b(3).\newlineb(4)=b(3)+12=17+12=29b(4) = b(3) + 12 = 17 + 12 = 29.

More problems from Arithmetic 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 8 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 8 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 8 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 (68)

Related topics

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