Question

A geometric sequence is defined recursively by a_n=3a_n-1. The 1st term of the sequence is 2.7. Write the explicit formula for the sequence.





A geometric sequence is defined recursively by . The 1st term of the sequence is 2.7. Write the explicit formula for the sequence.





A geometric sequence is defined recursively by . The 1st term of the sequence is 2.7. Write the explicit formula for the sequence.

Answer 1

You know what 'explicit formula' means? :)

Answer 2

it helps you find the value of a certain term in a geometric sequence??

Answer 3

Well, technically, the recursive formula also helps. However, a recursive formula usually involves previous terms of the sequence. Like, the recursive formula in the first...
\[\Large a_n = 3a_{n-1}\]
In other words, every term is 3 times the previous term.

An explicit formula, however, defines each term \(\large a_n\) as a function of n only, and not as a function of previous terms...
\[\Large a_n = f(n)\]

Answer 4

Okay, let's try another tack... the first term is 2.7, yes? :)

Answer 5

yesss.

Answer 6

What is the second term?

Answer 7

doesn't say

Answer 8

Of course it doesn't, but you can find it out by just reading the recursive formula...

Answer 9

I'm sooo sorry but I am confused

Answer 10

\[\Large a_n = 3a_{n-1}\]

Answer 11

yes, I know that I am suppose to use that

Answer 12

Well, I suggest you do :P\[\Large a_1 = 2.7\]

Answer 13

oh is it a_n=2.7*3^n-1

Answer 14

As a matter of fact, yes.

Answer 15

Looks like you got it already... good job.

Answer 16

alrighty. thank you :)