Question

After the first term in a sequence, the ratio of each term to the preceding term is r. If the first term is a, what is the third term?


(15 POINTS AND FREE BRAINIEST ANSWER!!)

Answer 1

first term is a₁.  Second term I call a₂.  We know that a₂/a₁ = r.  The third term is a₃ and we know also that a₃/a₂ = r.  Set these r's equal
a₃/a₂ = a₂/a₁.  solve for a₃ : a₃ = (a₂)²/a₁.  Or a₃ = a₂r

Answer 2

The third term is,$a_3=a_2r$

Suppose that the first term is a₁.

and the Second term call a₂.  

What is the common difference?

Suppose that the first term is $a_1$ and second term is  $a_2$  then the conman difference can be calculated by,

$a_2/a_1 = r.$

The third term is a₃ and we know also that $a_3/a_2 = r.$

Set these r's equal

$a_3/a_2 = a_2/a_1$

solve for a₃ : a₃ = (a₂)²/a₁

$a_3=\frac{(a_2)^{2} }{a_1} \\a_3=a_2r......since (\frac{a_2}{a_1})=r$

Therefore we get,the third term is,$a_3=a_2r$

To learn more about the sequence visit:

https://brainly.com/question/6561461