14.05.2022

2 to the power minus 6 as a fraction

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Step-by-step answer

09.07.2023, solved by verified expert

Faq

Mathematics
Step-by-step answer
P Answered by Specialist

\frac{1}{64}

Step-by-step explanation:

2^{-6}

= \frac{1}{2^{6}}

= \frac{1}{64}

Mathematics
Step-by-step answer
P Answered by PhD

S_7=6554

Step-by-step explanation:

The given series is 2-8+32-...

The first term of the sequence is

a_1=2

There is a common ratio of

r=-4

The sum of the first n terms of a geometric sequence is given by the formula;

S_n=\frac{a_1(1-r^n)}{1-r}

We want to find the first seven terms so n=7

We substitute the given values into the formula to obtain;

S_7=\frac{2(1-(-4)^7)}{1--4}

S_7=\frac{2(1--16384)}{1--4}

S_7=\frac{2(16385)}{5}

S_7=2(3277)

S_7=6554

The correct answer is A

Mathematics
Step-by-step answer
P Answered by PhD

n = 6

Step-by-step explanation:

Givens

r = 4

a = 2

Sum = 2730

Equation

Sum = a(1 - r^n)/(1 - r)

Solution

2730 = 2 (1 - 4^n) / (1 - 4)      Reduce the denominator

2730 = 2(1 - 4^n)/-3                Multiply both sides by -3

2730*-3 = 2(1 - 4^n)                Simplify the left

-8190 = 2(1 - 4^n)                    Divide by 2

-8190/2 = 1 - 4^n                     Simplify

-4095 = 1 - 4^n                         Subtract 1 from both sides.

-4096 =  - 4^n                            Divide by - 1

4096 = 4^n                                This looks like n is fairly large. You could use logs. Try n = 6.

4^6 does equal 4096              So your answer is 6.

Let's try it with logs. Ignore this if you don't know how to do this.

log(4096) = log(4)^n

log(4096) = n*log(4)                    Divide by log 4

log(4096)/log(4) = n

3.6124 / 0.6021  = n

n = 6

The hint is very helpful. Make sure you can follow it through

Mathematics
Step-by-step answer
P Answered by PhD

S_7=6554

Step-by-step explanation:

The given series is 2-8+32-...

The first term of the sequence is

a_1=2

There is a common ratio of

r=-4

The sum of the first n terms of a geometric sequence is given by the formula;

S_n=\frac{a_1(1-r^n)}{1-r}

We want to find the first seven terms so n=7

We substitute the given values into the formula to obtain;

S_7=\frac{2(1-(-4)^7)}{1--4}

S_7=\frac{2(1--16384)}{1--4}

S_7=\frac{2(16385)}{5}

S_7=2(3277)

S_7=6554

The correct answer is A

Mathematics
Step-by-step answer
P Answered by PhD

n = 6

Step-by-step explanation:

Givens

r = 4

a = 2

Sum = 2730

Equation

Sum = a(1 - r^n)/(1 - r)

Solution

2730 = 2 (1 - 4^n) / (1 - 4)      Reduce the denominator

2730 = 2(1 - 4^n)/-3                Multiply both sides by -3

2730*-3 = 2(1 - 4^n)                Simplify the left

-8190 = 2(1 - 4^n)                    Divide by 2

-8190/2 = 1 - 4^n                     Simplify

-4095 = 1 - 4^n                         Subtract 1 from both sides.

-4096 =  - 4^n                            Divide by - 1

4096 = 4^n                                This looks like n is fairly large. You could use logs. Try n = 6.

4^6 does equal 4096              So your answer is 6.

Let's try it with logs. Ignore this if you don't know how to do this.

log(4096) = log(4)^n

log(4096) = n*log(4)                    Divide by log 4

log(4096)/log(4) = n

3.6124 / 0.6021  = n

n = 6

The hint is very helpful. Make sure you can follow it through

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