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Oliga [24]
3 years ago
14

This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .

Mathematics
1 answer:
nasty-shy [4]3 years ago
5 0

True. A series is arithmetic if its terms come from an arithmetic sequence.

And a sequence is said to be arithmetic any of its two consecutive terms differ by a fixed difference, common to any consecutive pair.

As you can see, in this case, all terms differ by 2, so the sequence

6,\ 8,\ 10,\ 12,\ \ldots,\ 4+2n

is arithmetic, and thus the series

6 + 8 + 10 + 12 + \ldots + (4+2n)

is arithmetic as well.

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Answer:

  12. (x, D, E, F) = (8, 38°, 75°, 67°)

  13. (x, P, Q, R) = (13, 126°, 30°, 24°)

Step-by-step explanation:

The sum of angles in a triangle is 180°. We choose to write the equations assuming all measures are degrees.

12. (5x -2) +(9x +3) +(11x -21) = 180

  25x = 200 . . . . . . . add 20, simplify

  x = 8 . . . . . . . . . divide by 25

Then the angle measures are ...

  ∠D = 5(8) -2 = 38°

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13. (10x -4) +(4x -22) +(x +11) = 180

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  x = 13 . . . . . . . . . divide by 15

Then the angle measures are ...

  ∠P = 10(13) -4 = 126°

  ∠Q = 4(13) -22 = 30°

  ∠R = 13 +11 = 24°

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