Sagot :
COMMON RATIO OF A GEOMETRIC SEQUENCE
If [tex]S_{5}[/tex] = 189, [tex]a_{1}[/tex] = 3 and [tex]a_{5}[/tex] = 243, what is the common ratio in the sequence?
FORMULA:
[tex]r = \sqrt[4]{ \frac{b}{a} } [/tex]
where:
r = is the common ratio
a = is the first term
b = is the last term
SOLUTION:
- Substitute the given first and last extreme.
[tex]r = \sqrt[4]{ \frac{243}{3} } \\ \\ r = \sqrt[4]{81} \\ \\ r = 3[/tex]
ANSWER:
The common ratio is 3.
- To check, just multiply the common ratio by each terms.
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
81 × 3 = 243 ✔︎
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