What is the exact solution of e^x + 3 = 20

In an arithmetic sequence, the nth term an is given by the formula an=a1+(n−1)d, where a1 is the first term and d is the commo

Dmitry_Shevchenko [17]

Answer:

$a_{10} = \frac{10}{65536}$

Step-by-step explanation:

The first step to solving this problem is verifying if this sequence is an arithmetic sequence or a geometric sequence.

This sequence is arithmetic if:

$a_{3} - a_{2} = a_{2} - a_{1}$

We have that:

$a_{3} = 40, a_{2} = 10, a_{3} = \frac{5}{2}$

$a_{3} - a_{2} = a_{2} - a_{1}$

$\frac{5}{2} - 10 = 10 - 40$

$\frac{-15}{2} \neq -30$

This is not an arithmetic sequence.

This sequence is geometric if:

$\frac{a_{3}}{a_{2}} = \frac{a_{2}}{a_{1}}$

$\frac{\frac{5}[2}}{10} = \frac{10}{40}$

$\frac{5}{20} = \frac{1}{4}$

$\frac{1}{4} = \frac{1}{4}$

This is a geometric sequence, in which:

The first term is 40, so $a_{1} = 40$

The common ratio is $\frac{1}{4}$ , so $r = \frac{1}{4}$ .

We have that:

$a_{n} = a_{1}*r^{n-1}$

The 10th term is $a_{10}$ . So:

$a_{10} = a_{1}*r^{9}$

$a_{10} = 40*(\frac{1}{4})^{9}$

$a_{10} = \frac{40}{262144}$

Simplifying by 4, we have:

$a_{10} = \frac{10}{65536}$

3 0

3 years ago

I need help, help me plz !!!!! Match the verbal expression (term) with its algebraic expression (definition). Match Term Definit

Talja [164]

Answer:

Four less than an unknown value E) $y-4$

Quotient of a variable and four B) $\frac{z}{4}$

Some number to the power of four A) $a^4$

Four times an unknown value D) $4x$

Four more than some number C) $b+4$

Step-by-step explanation:

Let's analyze each statement separately:

- Four less than an unknown value --> this means that we have to subtract 4 to an unknown value. Calling $y$ the unknown value, it means we have to write

$y-4$

- Quotient of a variable and four --> this means we have to divide a variable by 4. Calling $z$ the unknown variabl, it means we have to write

$\frac{z}{4}$

- Some number to the power of four --> this means that we have to write the power of a number, in the form $a^m$ , where m in this case is equal to 4. Calling $a$ the unknown number, it means we have to write