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ser-zykov [4K]
3 years ago
15

Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...

Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Answer:

  • a_{12}=-244140625

Step-by-step explanation:

Considering the geometric sequence

5,-25,\:125,\:...

a_1=5

As the common ratio 'r' between consecutive terms is constant.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}

r=\frac{-25}{5}=-5

r=\frac{125}{-25}=-5

The general term of a geometric sequence is given by the formula:  

a_n=a_1\cdot \:r^{n-1}

where a_1 is the initial term and r the common ratio.

Putting n = 12 , r = -5 and a_1=5 in the general term of a geometric sequence to determine the 12th term of the sequence.

a_n=a_1\cdot \:r^{n-1}

a_n=5\left(-5\right)^{n-1}

a_{12}=5\left(-5\right)^{12-1}

      =5\left(-5^{11}\right)

\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a

       =-5\cdot \:5^{11}

\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}

        =-5^{1+11}     ∵ 5\cdot \:5^{11}=\:5^{1+11}

        =-244140625

Therefore,

  • a_{12}=-244140625
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Step-by-step explanation:

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3 years ago
Day Drive 270 miles and 6 hours how many miles do you drive in 13 hours ​
NikAS [45]

Answer:

The answer is

<h2>585 miles</h2>

Step-by-step explanation:

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From the question

Day Drive 270 miles in 6 hours

So in order to find the distance drove in 13 hours, we compare the distance drove in 6 hours to the distance drove in 13 hours and solve

That's

if in 6 hours Day drove 270 miles

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7 0
2 years ago
HELP WHAT IS THE ANSWERS
Temka [501]

Answer:   Letter Choice, (B)  ====>  4,256 pi cm^2


Step-by-step explanation:

<u>Formula: Surface Area of Cylinder  =   (2pi ) (r^2 )   +  2pi (r) (h)</u>



<u>Showing Work:</u>

<u>Radius  of the Base ===>  28cm</u>

<u>Height  =====>  48cm </u>

(2pi ) (r^2)    +   2pi (28)(48)

2 (pi) (r^2)     +    (circumference) (height)

2( pi) (r^2      +    2)( pi)(r)(h)

2 pi * (2) (r^2      +    (2)(r)(h)

2pi * (r^2        +       rh)

2(r)(pi)(r           +         h)

2( 28)(pi)(28       +       48)

56(pi)(76)

4256(pi)^2

<u>Therefore, Your Answer  ======>   Letter Choice; (B)  ======>  4,256pi cm^2</u>





Hope that helps!!!!!                                       : )


3 0
3 years ago
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