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:

Use the explicit formula to find a recursive formula for the sequence aa. Write your answer in simplest form. The recursive formula should depend on aa. \newlinea=−19n−40a = -19n - 40\newlinea = ______

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Convert an explicit formula to a recursive formularight chevron icon

Full solution

Q. Use the explicit formula to find a recursive formula for the sequence aa. Write your answer in simplest form. The recursive formula should depend on aa. \newlinea=−19n−40a = -19n - 40\newlinea = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−19n−40a = -19n - 40 involves a linear term in nn without any exponents, which indicates that the sequence is arithmetic.
  2. Find First Term: Find the first term of the sequence using the explicit formula.\newlineTo find the first term, substitute n=1n = 1 into the explicit formula:\newlinea1=−19(1)−40a_1 = -19(1) - 40\newlinea1=−19−40a_1 = -19 - 40\newlinea1=−59a_1 = -59
  3. Find Second Term: Find the second term of the sequence using the explicit formula.\newlineTo find the second term, substitute n=2n = 2 into the explicit formula:\newlinea2=−19(2)−40a_2 = -19(2) - 40\newlinea2=−38−40a_2 = -38 - 40\newlinea2=−78a_2 = -78
  4. Find Common Difference: Find the common difference in the arithmetic sequence.\newlineThe common difference dd can be found by subtracting the first term from the second term:\newlined=a2−a1d = a_2 - a_1\newlined=−78−(−59)d = -78 - (-59)\newlined=−78+59d = -78 + 59\newlined=−19d = -19
  5. Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.\newlineThe recursive formula for an arithmetic sequence is an=an−1+da_n = a_{n - 1} + d. Substitute −19-19 for dd in the formula:\newlinean=an−1−19a_n = a_{n - 1} - 19

More problems from Convert an explicit formula to a recursive 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 2 months ago

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

Posted 1 month 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 1 month 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 1 month 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 1 month 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 1 month 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 2 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 1 month ago

View all (19)