The first ten terms of the sequence $a_n=1 + (-\frac{4}{9} )^n$ is<em> 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003</em>

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

$a_n=1 + (-\frac{4}{9} )^n\\\\When\ n=1:a_1=1 + (-\frac{4}{9} )^1=0.5556\\\\When\ n=2:a_2=1 + (-\frac{4}{9} )^2=1.1975\\\\When\ n=3:a_3=1 + (-\frac{4}{9} )^3=0.9122\\\\When\ n=4:a_4=1 + (-\frac{4}{9} )^4=1.039\\\\When\ n=5:a_5=1 + (-\frac{4}{9} )^5=0.9827\\\\When\ n=6:a_6=1 + (-\frac{4}{9} )^6=1.0077\\\\When\ n=7:a_7=1 + (-\frac{4}{9} )^7=0.9966\\\\When\ n=8:a_8=1 + (-\frac{4}{9} )^8=1.0015\\\\When\ n=9:a_9=1 + (-\frac{4}{9} )^9=0.9993\\\\$

$When\ n=10:a_{10}=1 + (-\frac{4}{9} )^{10}=1.0003\\$

The first ten terms of the sequence $a_n=1 + (-\frac{4}{9} )^n$ is<em> 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003</em>

Find out more on equation at: brainly.com/question/2972832

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3 0

2 years ago

Patrick left an $8 tip on a $50 restaurant bill. What percent tip is that?

Gnoma [55]

Do 50 multiplied by x = 8. Solve for x.
It would give you .16 which is 16%.

3 0

3 years ago

Can someone please solve this.

Ksju [112]

Answer:

see explanation

Step-by-step explanation:

Given

(x² + 3)² + 21 = 10x² + 30 ← factor out 10 from each term on the right side

(x² + 3)² + 21 = 10(x² + 3) ← subtract 10(x² + 3) from both sides

(x² + 3)² - 10(x² + 3) + 21 = 0

Substituting u = x² + 3 into the equation gives

u² - 10u + 21 = 0 → D

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Using u² - 10u + 21 = 0 to solve the equation

Consider the factors of the constant term (+ 21) which sum to give the coefficient of the u- term (- 10)

The factors are - 3 and - 7, since

- 3 × - 7 = 21 and - 3 - 7 = - 10, thus

(u - 3)(u - 7) = 0

Equate each factor to zero and solve for u

u - 3 = 0 ⇒ u = 3

u - 7 = 0 ⇒ u = 7

We now have to use the substitution to convert the solutions into terms of x, that is

x² + 3 = 3 ( subtract 3 from both sides )

x² = 0 ⇒ x = 0 → D

x² + 3 = 7 ( subtract 3 from both sides )

x² = 4 ( take the square root of both sides )

x = ± $\sqrt{4}$ = ± 2

Thus x = - 2 → C

x = 2 → E

4 0

3 years ago