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:

What kind of sequence is this?\newline28,22,16,10,…28, 22, 16, 10, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Classify formulas and sequencesright chevron icon

Full solution

Q. What kind of sequence is this?\newline28,22,16,10,…28, 22, 16, 10, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences for Arithmetic: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 28,22,16,10,…28, 22, 16, 10, \ldots\newlineCalculate the differences: 22−28=−622 - 28 = -6, 16−22=−616 - 22 = -6, 10−16=−610 - 16 = -6.
  2. Common Difference Found: Since the differences between consecutive terms are equal, we can conclude that the sequence has a common difference of −6-6.
  3. Check Ratios for Geometric: An arithmetic sequence is defined by having a constant difference between consecutive terms. Since we have found a common difference, this sequence is arithmetic.
  4. No Common Ratio Found: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Calculate the ratios: 2228\frac{22}{28}, 1622\frac{16}{22}, 1016\frac{10}{16}.
  5. Sequence Classification: Perform the calculations: 2228≈0.7857\frac{22}{28} \approx 0.7857, 1622≈0.7273\frac{16}{22} \approx 0.7273, 1016=0.625\frac{10}{16} = 0.625.
  6. Sequence Classification: Perform the calculations: 2228≈0.7857\frac{22}{28} \approx 0.7857, 1622≈0.7273\frac{16}{22} \approx 0.7273, 1016=0.625\frac{10}{16} = 0.625. Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence.
  7. Sequence Classification: Perform the calculations: 2228≈0.7857\frac{22}{28} \approx 0.7857, 1622≈0.7273\frac{16}{22} \approx 0.7273, 1016=0.625\frac{10}{16} = 0.625. Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence. A geometric sequence is defined by having a constant ratio between consecutive terms. Since the ratios are not constant, this sequence cannot be geometric.
  8. Sequence Classification: Perform the calculations: 2228≈0.7857\frac{22}{28} \approx 0.7857, 1622≈0.7273\frac{16}{22} \approx 0.7273, 1016=0.625\frac{10}{16} = 0.625. Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence. A geometric sequence is defined by having a constant ratio between consecutive terms. Since the ratios are not constant, this sequence cannot be geometric. Based on the calculations and definitions, the sequence is arithmetic but not geometric. Therefore, the correct choice is (A)(A) arithmetic.

More problems from Classify formulas and 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 (100)