Write the series using summation notation -2 + 4+ -8 + 16 + -32

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Write the series using summation notation -2 + 4+ -8 + 16 + -32

The formula is

[tex]\frac{a_1(1-r^n)}{1-r}[/tex]

a1=first term

n=which term

r=common ratio

we see the common ratio is -2

frs term is 1

and we go to 10th term so n=10

[tex]\frac{1(1-(-2)^{10})}{1-(-2)}[/tex]

[tex]\frac{1(1-1024)}{1+2}[/tex]

[tex]\frac{1(-1023)}{3}[/tex]

-341

the sum is -341

The next will be 64, -128 each on is * by 2 and switching from pos to neg

-4/2

Step-by-step explanation:

just take 4 and divide it by -2 and youll get the common ratio as-2

Hope it helps

The answer to this is B. " -1 , -2 , -4, - 8, -16 , -32

It's b. -1,-2,-4,-8,-16,-32

because

[tex]a_n=2a_{n-1} \mbox{ where } a_1=-1.\\ So\\ a_2=2a_1=-2\\ a_3=2a_2=-4\\ a_4=2a_3=-8\\ a_5=2a_4=-16\\ a_6=2a_5=-32.[/tex]

you multiply it by -2 each time

Explanation:

positive times negative = negative

negative times negative= positive

- 32 x -2 = 64

64 x -2 = -128

Step-by-step explanation:

Each item is multiplied by -2

the answer is,

-2, 4, -8, 16, -32, 64

Remark

You can find the answer to that by dividing any 2 consecutive terms putting the right one in the numerator and the left one in the denominator.

Forumula

ratio = right/left

right = - 8

left = 4

ratio = -8/4

ratio = -2

Any two numbers would work.

ratio = - 32/16 = - 2

Hello,

[tex]u_{1}= -2 \\ u_{2}= -2 *(-2)=(-2)^2 \\ u_{3}= (-2)^2 *(-2)=(-2)^3 \\ u_{4}= (-2)^3 *(-2)=(-2)^4 \\ ...\\ \boxed{u_{n}= (-2)^n} \\ [/tex]