alexwing285
contestada

What are the values of a1 and r of the geometric series?
1 + 3 + 9 + 27 + 81

A. a1=1 and r=1//3
B. a1=1/3 and r=1
C. a1=1 and r=3
D. a1=3 and r=1

Respuesta :

irspow
a1 or just a as it is in the equations is just the initial term of the sequence.  In this case a1=1

r is the common ratio which is that constant ratio found by dividing any term by the term preceding it...

In this case r=3/1=9/3=27/9=etc=3

So a1=1 and r=3, C. is your answer.
facundo3141592

We will see that the correct option is C:

a₁ = 1 and r = 3.

Working with geometric sequences.

For a geometric sequence, the recursive formula is:

[tex]a_n = a_{n-1}*r[/tex]

In this case, our sequence is:

1, 3, 9, 27, 81

So we have:

[tex]a_1 = 1\\a_2 = 3\\a_3 = 9\\a_4 = 28\\a_5 = 81[/tex]

So we already can see that the first term is 1, to get the value of r, the common factor, we need to take the quotient between consecutive terms of the sequence:

[tex]a_2/a_1 = 3/1 = 3\\\\a_3/a_2 = 9/3 = 3\\\\a_4/a_3 = 27/9 = 3\\\\...[/tex]

In this way, you can see that the common factor is r = 3

Thus the correct option is C:

a₁ = 1 and r = 3.

If you want to learn more about geometric sequences, you can read:

https://brainly.com/question/9300199

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