If Subway sells turkey sandwiches for $3.79 each, how many sandwiches can you buy for your 6 friends to share with $20.00

The geometric sequence a i a i a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 =8a, start subscr

frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0

3 years ago

Solve sec2theta + tantheta - 3 =0 for 0

Serhud [2]

Answer:

Ф = $\frac{\pi }{4} ,\frac{5\pi}{4}$

Step-by-step explanation:

It is a bit difficult to input the work here, so I uploaded an image

First we can use the trig identities to change sec²(Ф) to tan²(Ф) + 1
Then we can combine like terms
Then we can factor this as a polynomial function
Then we can set each term equal to zero and solve for Ф
The first term tan(Ф) - 2 = 0 has no solution because tan(Ф) ≠ -2 anywhere
The second term tan(Ф) - 1 = 0 has two solutions of $\frac{\pi}{4}$ and $\frac{5\pi}{4}$ so these are the solutions to the problem

7 0

3 years ago

What is the simplified answer to this problem 12 > -3x + 6

Verdich [7]

In this question, you're simplifying the inequality by solving for x.

Solve for x:

12 > -3x + 6

flip the equation:

-3x + 6 < 12

subtract 6 from both sides

-3x < 6

divide both sides by -3, while also flipping the inequality

x > -2

Answer:

x > -2

8 0

3 years ago

Plz help me i really need this i will give brainliest

Leno4ka [110]

Step-by-step explanation:

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8 0

2 years ago

Read 2 more answers

Find the indicated sum of each sequence S8 of -2,-13,-24,-35

valentina_108 [34]

Answer:

The sum of the arithmetic sequence is $S_{8}=-324$ .

Step-by-step explanation:

A sequence is a set of numbers that are in order.

In an arithmetic sequence the difference between one term and the next is a constant. In other words, we just add the same value each time infinitely.

If the first term of an arithmetic sequence is $a_1$ and the common difference is d, then the nth term of the sequence is given by:

$a_{n}=a_{1}+(n-1)d$

For the sequence

$-2,-13,-24,-35,...$

The pattern is continued by adding -11 to the last number each time.

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, $a_1$ and last term, $a_n$ , divide by 2 in order to get the mean of the two values and then multiply by the number of values, n

$S_{n}=\frac{n}{2}(a_{1}+a_{n})$

The sum of the arithmetic sequence is

$a_{8}=-2+(8-1)(-11)=-2-77=-79$

$S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324$

3 0

3 years ago