Math Sequences Problems and How to Solve Them

Define whether the sequences are arithmetic. If so, what is the recursive definition, and what is the next term in the sequences?
(a) $25, 20, 15, 10, \dots$
(b) $2, 4, 7, 12, 13, \dots$

Viper 312022-06-02

Fund the 52nd term

-2, -6, -18, -54

Case Nixon 2022-05-31

Find the $a_{0}, a_{1}, a_{2}$ , and $lim a_{n}$ for the following sequences: $3 \times 10 = 30$
1) $a_{n} = (7 + 3 n) / (5 - 2 n)$
2) $a_{n} = (8 n) / (9 - n^{2})$
3) $a_{n} = 1 / 2 a_{n} + 8 / a_{n} (a_{0} = 1 g i v e n)$

Carlie Fernandez 2022-05-28

Find a recurrence relation for the number of n-digit (n greater or equal to 1) ternary sequences without an occurrence of the substring 012.

Pitrellais 2022-05-28

Write the first four terms of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why.
$a_{n} = 1 - 10^{- n}; n = 1, 2, 3, . . .$

seiyakou2005n1 2022-05-28

Write the first 4 terms of these geometric sequences
1) $a_{1} = - 3, r = - 5$
2) $a_{1} = \frac{1}{4}, r = 2$

Justine bernabe2022-05-26

bs1tuaz 2022-05-26

Find the limit of the following sequence:
$a_{n} = n / n + 5$

Isaiah Farrell 2022-05-21

Consider the sequences $a_{n}$ and $b_{n}$ , where
$a_{n} = \frac{n (2 n + 1)}{n^{2}}$ and $b_{n} = \frac{(- 1)^{n}}{5}$

Which of the sequences converge and which diverge? If it converges, indicate its limit

Davin Fields 2022-05-19

Write the terms $a_{1}, a_{2}, a_{3},$ and $a_{4}$ of the following sequence. If the sequence converges, make a conjecture about its limit.
$a_{n + 1} = 10 a_{n} - 1; a_{0} = 0$

Gael Gardner 2022-05-19

Please, list the first 5 terms $(x_{1}, x_{2}, x_{3}, x_{4}, x_{5})$ of the sequences
$a) x_{n} = 3 n^{2} - 5$
$b) x_{1} = 4, x_{n + 1} = 7 - x_{n}$

Yasmin Camacho 2022-05-19

Identify if the sequence is arithmetic, geometric, or neither of the two. Find the next three terms of the sequence.
2, 3, 5, 9, 17, 33, ...

Aedan Gonzales 2022-05-13

How many terms are there in each of the sequences?
$a . 56, 57, 58, 59, . . ., 456$
$b .1, 5, 5^{2}, 5^{3}, . . ., 5^{40}$
$c . 100, 200, 300, 400, . . ., 40000$
$d . 1, 3, 9, 27, 81, 243, . . ., 6561$

Jamir Melendez 2022-05-12

Which of these sequences are geometric sequences?

1) $2, 4, 8, 16, 32, 64, 128, . . .$
2) $100, - 50, 25, - 12.5, 6.25, - 3.125, 1.5625, - 0.78125, . . .$
3) $1, 1, 2, 3, 5, 8, 11, . . .$
4) $3, 6, 9, 12, 15, 18, 21, \dots$

Dennis Montoya 2022-05-12

Which of the following sequences are convergent sequences?
1) $a_{n} = \frac{7^{n}}{n^{7}}$
2) $a_{n} = \frac{1}{n}$
3) $a_{n} = \frac{1}{7} + (- 1)^{n}$
4) $a_{n} = \frac{\cos (n)}{n}$
5) $a_{n} = 7$
6) $a_{n} = 7$

Find the 87th term of the arithmetic sequence $12, 0, -12, ...$ 12,0,−12,…

Maximillian Patterson 2022-05-01

Prove that $lim_{n \Rightarrow \infty} \frac{n}{2 n - 1} = \frac{1}{2}$

Philip Ramirez 2022-05-01

Please, find the limit superior and limit inferior of each of the following sequences
1) $(x_{n}) = (n \cos (\frac{n π}{2})), n \in N$
2) $(x_{n}) = (n \cos^{2} (\frac{n π}{2})), n \in N$
3) $(x_{n}) = ({(- 1)}^{n} - \frac{n}{n + 1}), n \in N$

Ellie Castro 2022-04-30

Please, conclude by the Bounded Convergence Theorem that the sequence is convergent $\neq^{- n}$

hapantad2j 2022-04-30

Prove:
$lim_{n \Rightarrow \infty} \ln (\frac{n + 1}{n}) = 0$

In the majority of cases, solving Math sequences problems is a constant task of data programmers, architects, and engineers who construct furniture, aircraft, automobiles, or program automation for robotics. Even if you have used some Math sequences solver before, it’s essential to start with at least one equation that will help you to set your variables straight and create the foundation for a sequence. While you read your instructions, do not forget to compare them with provided answers to sequences of Math problems below. These will help you with the basics and explain the structure of sequences in various applications.

Algebra I

Solve Sequences Math Problems with Us