Answered

if s5= 189, a1= 3, a5= 243. What is the common ratio in the sequence?​

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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