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?\newline81,100,121,144,…81, 100, 121, 144, \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
Grade 8right chevron icon
Identify arithmetic and geometric sequencesright chevron icon

Full solution

Q. What kind of sequence is this?\newline81,100,121,144,…81, 100, 121, 144, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences: Now, let's check if the differences are the same, which is a requirement for an arithmetic sequence.\newlineDifference between terms are: 1919, 2121, and 2323.\newlineSince the differences are not constant, this is not an arithmetic sequence.
  2. Check Ratios: Next, let's check if it's a geometric sequence by finding the ratio between consecutive terms.\newlineRatio between second and first term: 10081\frac{100}{81}\newlineRatio between third and second term: 121100\frac{121}{100}\newlineRatio between fourth and third term: 144121\frac{144}{121}
  3. Calculate Ratios: Now, let's calculate the ratios to see if they are the same, which is a requirement for a geometric sequence.\newlineRatio between second and first term: 10081≈1.2346\frac{100}{81} \approx 1.2346\newlineRatio between third and second term: 121100=1.21\frac{121}{100} = 1.21\newlineRatio between fourth and third term: 144121≈1.1901\frac{144}{121} \approx 1.1901\newlineSince the ratios are not constant, this is not a geometric sequence.
  4. Conclusion: Since the sequence is neither arithmetic (because the differences are not constant) nor geometric (because the ratios are not constant), we can conclude the type of sequence.\newlineThe sequence is neither arithmetic nor geometric.

More problems from Identify arithmetic and geometric 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 (33)