I don't understand. If a_n is a sequence that includes the terms:
250, ___, 10
What missing number(s) would the missing term be if:

a) a_n is arithmetic
b) a_n is geometric

9514 1404 393

Step-by-step explanation:

Arithmetic sequence

The terms of an arithmetic sequence have common difference. If the missing term is x, then the difference between terms is the same:

  x -250 = 10 -x

  2x = 260 . . . . . . add 250+x to both sides

  x = 130 . . . . . . . . divide by 2

The missing term of an arithmetic sequence is 130.

(the common difference is -120)

__

Geometric sequence

The terms of a geometric sequence have a common ratio. If the missing term is x, then the ratios between terms are the same:

  x/250 = 10/x

  x^2 = 2500 . . . . . . . multiply both sides by 250x

  x = ±√2500 = ±50 . . . take the square root

The missing term of a geometric sequence is +50 or -50.

(the common ratio is ±1/5)

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