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Answer:
see explanation
Step-by-step explanation:
The common ratio r of a geometric sequence is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = .....
r = [tex]\frac{-20}{8}[/tex] = [tex]\frac{50}{-20}[/tex] = - 2.5
Multiplying each term by - 2.5 gives the next term
50 × - 2.5 = - 125
- 125 × - 2.5 = 312.5
312.5 × - 2.5 = - 781.25
The next 3 terms in the sequence are - 125, 312.5, - 781.25
The common ratio is -2.5
Next 3 terms after 50 are -125, 312.5, -781.25
What is a geometric sequence and common ratio?
A sequence ( increasing or decreasing) having a pattern that the next term is found by multiplying the previous term with a constant term called common ratio, is called a geometric sequence. Common ratio can be positive or negative.
- Common ratio can be found by dividing a term by its previous term.
How to find the common ratio of the given geometric sequence?
The given sequence is 8, -20, 50......
The common ratio is [tex]\frac{-20}{8}= - 2.5[/tex]
How to find the next terms of the given geometric sequence?
- In a geometric sequence, a term multiplied by the common ratio gives ithe next term.
Next term after 50 = {50 x (-2.5)} = -125
Next term after -125 = {(-125) x (-2.5)} = 312.5
Next term after 312.5 = {312.5 x (-2.5)} = -781.25
- Next 3 terms after 50 are -125, 312.5, -781.25
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