9514 1404 393
Answer:
- arithmetic: 130
- geometric: ±50
Step-by-step explanation:
<u>Arithmetic sequence</u>
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)
__
<u>Geometric sequence</u>
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)
