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liubo4ka [24]
3 years ago
13

Arithmetic sequence

Mathematics
1 answer:
HACTEHA [7]3 years ago
8 0

Answer:18

Step-by-step explanation:

Note: Mathematicians start counting at 1, so by convention, n=1 is the first term. So we must define what the first term is. Then we have to figure out and include the common difference.

Taking a look at the examples again,

Sequence: 1, 2, 3, 4, … | Formula: a(n) = n + 1 | Recursive formula: a(n) = a(n-1) + 1, a(1) = 1

Sequence: 3, 8, 13, 18, … |Formula: b(n) = 5n - 2 | Recursive formula: b(n) = b(n-1) + 5, b(1) = 3

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In an arithmetic sequence, the 10th term is 37, and the 21st term is 4. Find the common difference and the first term
Masja [62]

Answer:

Common difference is 3. And the first term is 64.

Step-by-step explanation:

The differnce between 21 and 10 is 11. So there are 11 unknown numbers in between.  And the difference between 37 and 4 is 33. 33/11 is equal to 3. So the pattern is minus three. the first term is 9 terms before 37. 9 times 3 is 27. 37+27 is equal to 64. so the first term is 64

3 0
3 years ago
PLEASE! Is this correct?
Paladinen [302]
I believe it’s correct, but i’m not smart
6 0
3 years ago
Can someone help me
erik [133]

Answer:

   6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

  (2x -12)/2 = arcsin(16/22×sin(24°))

  x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

  2x -12 = 0

  x -6 = 0 . . . . . divide by 2

  x = 6 . . . . . . . add 6

Then the range of values of x will be ...

  6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

  22² = AB² + AC² -2·AB·AC·cos(48°)

  16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

  22² = 2·AB²·(1-cos(48°))

  16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0
2 years ago
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What set of reflections would carry hexagon ABCDEF onto itself?
k0ka [10]

Answer:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Step-by-step explanation:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

8 0
2 years ago
A toy train makes 10 laps around a track in 12 minutes. hpw me my laps per hour is that.
marusya05 [52]

Answer:

50

Step-by-step explanation:


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3 years ago
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