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motikmotik
2 years ago
14

We are given a sequence of five non-zero numbers, where the sum of each term and its neighboring terms is 15 or 25. Find the sum

of all the terms in the sequence.
Mathematics
1 answer:
PSYCHO15rus [73]2 years ago
3 0

We have a sequence that meets the given criteria, and with that information, we want to get the sum of all the terms in the sequence.

We will see that the sum tends to infinity.

So we have 5 terms;

A, B, C, D, E.

We know that the sum of each term and its neighboring terms is 15 or 25.

then:

  • A + B + C = 15 or 25
  • B + C + D = 15 or 25
  • C + D + E = 15 or 25

Now, we want to find the sum of all the terms in the sequence (not only the 5 given).

Then let's assume we write the sum of infinite terms as:

a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + ...

Now we group that sum in pairs of 3 consecutive terms, so we get:

(a_1 + a_2 + a_3) + (a_4 + a_5 + a_6) + ...

So we will have a sum of infinite of these, and each one of these is equal to 15 or 25 (both positive numbers). So when we sum that infinite times (even if we always have the smaller number, 15) the sum will tend to be infinite.

Then we have:

(a_1 + a_2 + a_3) + (a_4 + a_5 + a_6) +  ... \to \infty

If you want to learn more, you can read:

brainly.com/question/21885715

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3 years ago
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What’s the rest of the qurstion?
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3 years ago
Find the distance between each set of points. Round to the nearest tenth, when necessary. (-3, 2) and (1, -6)
vovangra [49]

Answer:

<h2>The answer is 8.9 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

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From the question the points are

(-3, 2) and (1, -6)

The distance between them is

d =   \sqrt{ ({ - 3 - 1})^{2}  +  ({2 + 6})^{2} }   \\  =  \sqrt{ ({ - 4})^{2} +  {8}^{2}  }  \\  =  \sqrt{16 + 64}  \\  =  \sqrt{80}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 4 \sqrt{5}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 8.9442719...

We have the final answer as

8.9 units to the nearest tenth

Hope this helps you

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3 years ago
Simplify to create an equivalent expression.
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3 years ago
Read 2 more answers
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AleksAgata [21]


3/12% = 25

<em>Therefore, 3 is 12% of 25.</em>

3 0
3 years ago
Read 2 more answers
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