Math Sequences Problems and How to Solve Them

Please, show that the sum and the product of two Cauchy sequences are Cauchy sequences.

pettingyg0 2022-04-24

If $P = 8 + 10 + 12 + 14 + \dots + 108$ and $Q = 4 + 6 + 8 + 10 \dots + 106$ are sums of arithmetic sequences, determine which of them is greater.

Bruce Rosario 2022-04-22

We have the sequence $31, 27, 23, 19$ . How you can get the next three numbers

yopopolin10d 2022-04-22

We have the sequence ${0, 1, 2, 3, 3, 4, 6, 9, 8, \dots}$ for which we have to find the summation of terms to the nth term, $C_{n}$
However, the number of terms in the sub sequence, $N \neq n$ , the number of terms in the larger sequence. What is a way to represent N in terms of n in order to arrive at a single formula for $C_{n}$ ? I've determined that it can be $N = \frac{n}{3}$ but this is only true for cases where n is a multiple of 3. How do I find those two cases where n isn't a multiple of 3?

hestyllvql 2022-04-20

If convergent sequences are bounded and convergent sequences are Cauchy sequences, can't you conclude that Cauchy sequences are bounded? If it's true, please, prove it.

Terrence Moore 2022-04-20

How many four-letter sequences are possible that use the letters "q, u, a, k, e, s" at most once each?

Boston Fitzgerald 2022-04-18

We know that convergent sequences approximate certain numbers. For example, the sequence $\frac{1}{2}, \frac{1}{2} + \frac{1}{4}, \frac{1}{2} + \frac{1}{4} + \frac{1}{8}, \dots$ etc approximates the number 1.
Are there sequences that approximate sequences?

Braden Hatfield 2022-04-15

Find the limit of the sequence
$a_{n} = \frac{5 n^{2} - 8 n + 11}{7 n + 4}$

Devin Dougherty 2022-04-15

Find the following sums of arithmetic sequences.
$881 + 872 + 863 + 854 + \dots .8$

Colten Welch 2022-04-13

Find the limit
$a_{n} = \frac{8 - 5 n}{7 n}$

George Michael 2022-04-13

Find $a_{5}$ and $a_{n}$ for the geometric sequences.
$a_{2} = 12$ , $r = \frac{1}{2}$

Tiffany Maldonado 2022-04-13

Find $a_{5}$ and $a_{n}$ for the geometric sequences:
$a_{1} = - 5$ , $r = - 7$

Deangelo Hardy 2022-04-12

How do you formulate Fibonacci Sequences? What is its relation to the concept of Golden Ratio, Golden Rectangle, Golden Angle and Golden Spiral?

Charlotte Holden 2022-04-12

Find the n-th term
$- 5, - 3, - 1, 1, \dots$

Bryson Whitney 2022-04-12

Find the false statement
1) $\sum_{n = 2}^{\infty} \frac{1}{n (\ln n) P}$ converges if $p > 1$
2) the integral test does not apply to divergent sequence
3) $\sum_{n = 1}^{\infty} \frac{1}{n P}$ converges if $p > 1$ and diverges if $p \leq 1$
4) If $a_{n}$ and $f (n)$ satisfy the requirements of the integral test, and if $\int_{1}^{\infty} f (x) d x$ converges, then $\sum_{n = 1}^{\infty} a_{n} = \int_{1}^{\infty} f (x) d x$

Angelina Kaufman 2022-04-12

Find formulas that describe the sequences
1) $4, 7, 10, 13, 16, 19, \dots$
2) $5, 7, 11, 19, 35, 67, \dots$

Rubi Riggs 2022-04-11

Use the approach in Gauss’s Problem and find the sums of following arithmetic sequences
(a) $1 + 2 + 3 + 4 + \dots + 999$
(b) $1 + 3 + 5 + 7 + \dots + 999$
(c) $8 + 17 + 26 + 35 + \dots + 881$
(d) $692 + 685 + 678 + 671 + \dots + 6$

Regina Ewing 2022-04-10

In the past, a local telephone number in a country consisted of a sequence of three letters followed by four digits. Three letters were associated with each number from 2 to 9 (just as in the standard telephone layout shown in the figure) so that each telephone number corresponded to a sequence of seven digits. How many different sequences of seven digits were possible?

Yaritza Oneill 2022-04-10

Write three terms that continue the arithmetic or geometric sequences. Define whether the sequences are arithmetic or geometric.
a) 1, 4, 7, 10, 13
b) 3, 9, 27, 81, 243
c) 11, 15, 19, 23 , 27

Frances Simon 2022-04-09

Use the following generating function to create a sequence using $n = 0, 1, 2, 3, 4$
$a_{n} = 2^{n + 1}$

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

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