Math Sequences Problems and How to Solve Them

Find the ﬁrst four terms of each of the recursively deﬁned sequences
$d_{k} = k {(d_{k - 1})}^{2}$ for all integers $k \geq 1$
$d_{0} = 3$

Vilharjevw7 2022-01-23

Find $a_{5}$ and $a_{n}$ for the geometric sequence.
$a_{3} = 2$ , $r = \frac{1}{3}$

Mlejd5 2022-01-23

Prove, using the definitio of a convergent sequence
$lim_{n \to \infty} \ln ({\frac{n}{n + 1}}) = 0$

logosomatw 2022-01-23

Use the approach in Gausss

Adrian Cervantes 2022-01-23

Find the limits of the following sequences
$a_{n} = n^{\frac{5}{n}}$

Lainey Goodwin 2022-01-23

Give an example of such $f (x)$ and prove, why it works
A non constant function $f : [0, 1] \to R$ such that $f (x) \geq 0$ for any $x \in [0, 1]$ , but $\int_{0}^{1} f (x) d x = 0$

Jazmin Perry 2022-01-23

We have the sequence $1, 2, 3, 5, 8$
What is the next number in the sequence?

Connor Randall 2022-01-23

For each of the sequences, write a formula for the general term. Use the formula to find $a_{20}$
1) $2, 7, 12, 17, \dots$
2) $6, 1, - 1, - 9, \dots$
3) $a_{0} = 4, d = - 0.3$
4) $a_{0} = \frac{3}{4}, d = - \frac{1}{4}$

Reese Munoz 2022-01-23

Give the first six terms of the following sequences.
1) $g_{1} = 2$ and $g_{2} = 1$
2) $c_{1} = 4, c_{2} = 5$ and $c_{n} = c_{n - 1} \times c_{n - 2}$ for $n \geq 3$
3) $b_{1} = 1, b_{2} = 3$ and $b_{n} = b_{n - 1} - b_{n - 2}$ for $n \geq 3$
4) $d_{1} = 1, d_{2} = 1$ and $d_{n} = {(d_{n - 1})}^{2} + d_{n - 2}$ for $n \geq 3$

Caleb Snyder 2022-01-23

Consider the sequences
a. ${a_{n}} = {- 2, 5, 12, 19, \dots}$
b. ${b_{n}} = {3, 6, 12, 24, 48, \dots}$
(a) Find the next two terms of the sequence.
(b) Find a recurrence relation that generates the sequence.
(c) Find an explicit formula for the nth term of the sequence.

tripplek7i 2022-01-23

Show that the following sequences converge
$a_{n} = 5 + \frac{1}{n}$

Jessie Jenkins 2022-01-23

Find the Z transform of the sequence
$3^{k} + {(- 3)}^{k} + 3 k$

Keaton Good 2022-01-23

How many sequences can be formed using all the letters in ARCANSAS?

David Rojas 2022-01-23

Solve the sequece, please
a) $\frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, ?, ?$
b) $1, 3, 6, 10, 15, 21, ?, ?$
c) $1, 4, 9, 16, 25, 36, ?, ?$
d) $1, 2, 4, 8, 16, 32, ?, ?$

Keaton Good 2022-01-23

If a die is rolled 30 times, there are $6^{30}$ different sequences possible.
What fraction of these sequences have exactly eight 1s and eight 6s?

Advadlippabrj 2022-01-23

Let ${x_{n}}_{n = 1}^{\infty}$ , and ${y_{n}}_{n = 1}^{\infty}$ be two sequences of positive numbers. Assume that $x_{n} ⟨ y_{n}$
For each one of the following claims, decide whether they are always true, always false, or sometimes true and sometimes false (depending on the specific sequences) and prove it.
1) $x_{n} ⟨ \frac{x_{n} + y_{n}}{2}$
2) $\frac{x_{n} + y_{n}}{2} ⟨ y_{n}$

Ella Bradshaw 2022-01-22

Find the sum of sequences
$5 + 7 + 9 + \dots + 137$

meteraiqn 2022-01-22

The following sequences' first ten terms should be given. Assume that the sequences are in base 2 and have an index of 1.
Indicate whether the sequence is increasing, decreasing, non-increasing, or non-decreasing.
1) The nth term is the largest integer k such that $k! \leq n$ .
2) The nth term is 1/n.
3) The nth term is 3.
4) The nth term is $n^{2}$ .
5) The nth term is [ $\log n$ ].

tripplek7i 2022-01-22

Possible head-tail sequences that can occur when you flip a coin three times.
(a) How many sequences contain exactly two heads?
(b) Probability extension: Assuming the sequences are all equally likely, what is the probability that you will get exactly two heads when you toss a coin three times?

siutulysr5 2022-01-22

Find the Z transform of the sequence
${k {(\frac{1}{2})}^{k}}$

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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