Solve Sequences Math Problems with Us

Complete the following quenstions involving definitions for sequences
Whitch of the following sequences is being generated by an "Explicit Formula"?
1)$a_n=\{n^2+3\}$
2)$a_n=\{5_n+7\}$
3)$a_n=\left\{\frac{2}{n+1}\right\}$
4)$a_{n+2}=\{a_n+1-3a_n\}$

Use what you know about bonded, monotonic sequences to show that the following sequences converge
$a_n=\frac{1}{3}(1-\frac{1}{3^n})$

Using the definition of a convergent sequence, prove
${\displaystyle \underset{n\to \mathrm{\infty }}{lim}{e}^{\left(\frac{n+1}{n}\right)}=e}$
${\displaystyle \left(\frac{n+1}{n}\text{is the exponent of e}\right)}$
Don't use any theorems about convergent sequences

For each of the following sequences, write a formula for the general term. Then use the formula to find ${\displaystyle a_{2}0}$
1) $2,7,12,17...$
2) $6,1,-1,9,...$
3) ${\displaystyle a_0=4,d=-0.3}$
4) $a_0=\frac{3}{4},d=-\frac{1}{4}$

Find the limits of the following sequences.
1) $\cos ((2n+1)\frac{\pi }{2}{)}_{n=1}^{\mathrm{\infty }}$
2) ${\frac{{\pi }^n}{e^{2n+1}}}^{\mathrm{\infty }}$

Identify, please, whether each phrase is an expression, inequality, or equation.
${\displaystyle 3–5x=y}$
${\displaystyle 7–5<2\times 9}$
${\displaystyle \frac{2+v}{t}}$

The equations $y=-x+4$ and $y=12x-8y=21x-8$ form a system of linear equations. The table below shows the y-value for each equation at six different values of x.

$xy=-x+4y=12x-804-822-740-66-2-58-4-410-6-3$
What can you conclude from the table?

A. The system has one solution, when $x=0$.

B. The system has one solution, when $x=4.$

C. The system has one solution, when $x=8.$

D. The system has no solution.

Solve the equations and inequalities:
${\displaystyle 2^x<30}$