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) Here are the first five terms of a different sequence. Find an expression for the nth term of this sequence. U_(1)=a=0 u_(2)=0+3 3+2(n-1)

(b) Here are the first five terms of a different sequence.\newlineFind an expression for the n n th term of this sequence.\newlineU1=a=0 U_{1}=a=0 \newlineu2=0+3 u_{2}=0+3 \newline3+2(n−1) 3+2(n-1)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Evaluate variable expressions for number sequencesright chevron icon

Full solution

Q. (b) Here are the first five terms of a different sequence.\newlineFind an expression for the n n th term of this sequence.\newlineU1=a=0 U_{1}=a=0 \newlineu2=0+3 u_{2}=0+3 \newline3+2(n−1) 3+2(n-1)
  1. Write Initial Terms: First, let's write down the first few terms we know.\newlineU1=a=0U_1 = a = 0\newlineU2=0+3=3U_2 = 0 + 3 = 3
  2. Identify Pattern: Now, let's look at the pattern. Each term seems to be 33 more than the previous one, starting from 00.
  3. Calculate Third Term: So, the third term would be U2+3=3+3=6U_2 + 3 = 3 + 3 = 6.
  4. Derive General Formula: The pattern suggests that each term is 33 times the position minus 33. Let's write that down.\newlineUn=3n−3U_n = 3n - 3
  5. Verify Formula with Known Terms: Let's check this formula with the terms we know.\newlineFor n=1n=1, U1U_1 should be 3(1)−3=03(1) - 3 = 0, which is correct.\newlineFor n=2n=2, U2U_2 should be 3(2)−3=33(2) - 3 = 3, which is also correct.
  6. Correct Pattern: But wait, the problem says the second term is 0+30 + 3, which is 33, and then it says to add 2(n−1)2(n-1) for the next terms. So the pattern is actually adding 22 to the previous term, not 33. Let's correct that.\newlineUn=2(n−1)U_n = 2(n - 1)

More problems from Evaluate variable expressions for number 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 3 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 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 2 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 2 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 2 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 2 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 2 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 3 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 2 months ago

View all (74)