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3 years ago

If the common difference in an arithmetic sequence is 4, and the 20th term is 36, what is the first term?

1 answer:

5 0

The sum of an arithmetic sequence can be found using the formula S = n/2(a + l) where S equals sum, n equals # terms, a equals the first term and l equals last term we know enough of these to find the missing pieces S = -15 n = 20 a = 4 -15 = 20/2 (4 + l) now we only have one unknown -15 = 10 (4 + l) -15 = 40 + 10l -55 = 10l l = -5.5 so the last term is -5.5 now we can use anothe formula to find the common difference l = a + (n-1) d so the last term equals the first term (a) plus # terms -1 times (d) the common difference -5.5 = 4 + (20-1) d -9.5 = 19 d d = -.5 so your common difference is -.5

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I didn't fully understand the question but this is the best I can do! Hope this helps! :D

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3 years ago

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victus00 [196]

Answer:

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Step-by-step explanation:

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3 years ago

Please choose the option that would best fit the empty space above: Group of answer choices only one optimal solution multiple o

Scrat [10]

Answer:

Follows are the solution to this question:

Step-by-step explanation:

In this question, some of the data is missing, that's why this question can be defined as follows:

It Includes an objective feature coefficient, its sensitivity ratio is the ratio for values on which the current ideal approach will remain optimal.

When there is Just one perfect solution(optimal solution) then the equation is:

$Max \ Z = \$ 5x_1 + \$10x_2\\\\Subject\ to: \\\\8x_1 + 5x_2 \leq 80\\\\2x_1 + 1x_2 \leq 100\\\\x1, x2 \geq 0$

When there are Several perfect solutions then the equation is:

$Max \ Z = \$ \ 200x_1 + \$ \ 100x_2\\\\ Subject \ to:\\\\8x_1 + 5x_2 \leq 80\\\\2x_1 + 1x_2 \leq 100\\\\x1, x2 \geq 0$

When there is also no solution, since it is unlikely then the equation is:

$Max \ Z = \$40x_1 + \$10x_2 \\\\Subject \ to:\\\\8x_1 + 5x_2 \leq 80\\\\2x_1 + 1x_2 \geq 100\\\\x_1, x_2 \geq 0$

When there is no best solution since it is unbounded then the equation is:

$Max \ Z = \$ 30x_1 + \$15x_2 \\\\Subject to:\\\\8x_1 + 5x_2 \geq 80\\\\2x_1 + 1x_2 \geq 100\\\\x_1, x_2 \geq 0\\$

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3 years ago

A 6.50% coupon bond with 18 years left to maturity is offered for sale at $1,035.25. What yield to maturity [interest rate] is t

Basile [38]

Answer:

The yield to maturity is 6.3974%

Step-by-step explanation:

The computation of the yield to maturity is as follows

Given that

NPER = 18 × 2 = 36

PMT = $1,035.25 × 6.50% ÷ 2 = $33.65

PV = $1,035.25

FV = $1,000

The formula is shown below:

=RATE(NPER;PMT;-PV;FV;TYPE)

The present value comes in negative

AFter applying the above formula, the yield to maturity is

= 3.1987% × 2

= 6.3974%

Hence, the yield to maturity is 6.3974%

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3 years ago