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NeTakaya
3 years ago
6

five consecutive terms of an arithmetic sequence have a sum of 40. The product of the middle and the two end terms is 224. Find

the terms of the sequence.
Mathematics
1 answer:
ratelena [41]3 years ago
4 0
Let the five terms be: a, a + d, a + 2d, a + 3d, a + 4d, then
a + a + d + a + 2d + a + 3d + a + 4d = 5a + 15d = 40
i.e. a + 3d = 8
Also, (a + 2d)(a + 3d)(a + 4d) = 224
(a + 3d - d)(a + 3d)(a + 3d + d) = 224
(8 - d)(8)(8 + d) = 224
(8 - d)(8 + d) = 224/8 = 28
64 - d^2 = 28
d^2 = 64 - 28 = 36
d = sqrt(36) = 6
But a + 3d = 8
a + 3(6) = 8
a = 8 - 18 = -10

Therefore, the term of the sequence is: -10, -10 + 6, -10 + 2(6), -10 + 3(6), -10 + 4(6)
= -10, -4, -10 + 12, -10 + 18, -10 + 24
= -10, -4, 2, 8, 14

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Westkost [7]

Answer:

-7.90

Step-by-step explanation:

Let's write the null hypothesis (H0) and alternative hypothesis (Ha) from the claim statement

P = population proportion of adults who would erase all of their personal information online if they could

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Let's write the given information:

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formula of z test statistic for one sample proportion test is as follows:

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plug the above values in the above formula we get

Z =\frac{0.35-0.5}{\sqrt{\frac{0.35(1-0.5)}{480}}}=Z=-7.85584

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3 0
3 years ago
What is the common difference between the elements of the arithmetic sequence below?
Tanya [424]
<h3> - - - - - - - - - - - - - ~<u>Hello There</u>!~ - - - - - - - - - - - - - </h3>

➷ -22.5 - (-18) = -4.5

-27 - (-22.5) = -4.5

The common difference is 4.5

➶Hope This Helps You!

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7 0
3 years ago
Two sides of a rectangle differ by 3.5cm.Find the dimensions of the rectangle if its perimeter is 67cm.
Margaret [11]

Answer:

Sides are x and x + 3.5 cm

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Step-by-step explanation:

HOPE THIS HELPED!

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