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3 years ago

Find the 8th term of the geometric sequence 7,−21,63,

Mathematics

2 answers:

finlep [7]3 years ago

5 0

Answer:

8th term is -15309

Step-by-step explanation:

${ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}$

r is the common difference, r = -21/7 = -3

noname [10]3 years ago

5 0

Answer:

a₈ = - 15309

Step-by-step explanation:

The nth term of a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 7 and r = $\frac{a_{2} }{a_{1} }$ = $\frac{-21}{7}$ = - 3 , then

a₈ = 7 × $(-3)^{7}$ = 7 × - 2187 = - 15309

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Elanso [62]

Answer:

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Step-by-step explanation:

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3 years ago

What is the equation, in standard form, of a parabola that contains the following points? (-2,18),(0,4),(4,24)

nydimaria [60]

Y=ax² + bx + c and A(-2,18), B(0.4), C(4,24) given

1)Let's determine 1st the value of c in using the pair of B
4= a(0)² + b(0) + c , c=4 and y=ax²+bx+4

2) Use the pair of A: 18 = 4a -2b + 4===> 4a-2b=14

3) Use C pair: 24 = 16a+4b+4 ==> 16a+4b=20

4) solve the system equation in 2) and 3) and you'll find a=2 and b=-3

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6 0

3 years ago

Solve for x in the equation x squared + 2 x + 1 = 17.

Papessa [141]

Answer:

$x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\$

Step-by-step explanation:

given equation

$x^2 +2x +1 = 17$

subtracting 17 from both sides

$x^2 +2x +1 = 17\\x^2 +2x +1 -17= 17-17\\x^2 +2x - 16 = 0\\$

the solution for quadratic equation

$ax^2 + bx + c = 0$ is given by

x = $x = -b + \sqrt{b^2 - 4ac} /2a \\\\and \ \\-b - \sqrt{b^2 - 4ac} /2a$

________________________________

in our problem

a = 1

b = 2

c = -16

$x =( -2 + \sqrt{2^2 - 4*1*-16}) /2*1 \\x =( -2 + \sqrt{4 + 64}) /2\\x =( -2 + \sqrt{68} )/2\\x = ( -2 + \sqrt{4*17} )/2\\x = ( -2 + 2\sqrt{17} )/2\\x = - 1 + \sqrt{17}\\and\\\\x = - 1 - \sqrt{17}\\$