How do you write an nth term rule for 1,-4,16,-64 and find a_6?

1 Answer
JMicheli
Aug 2, 2016

a_6 = 4096 or a_6 = -1024 depending on convention.

Explanation:

The series here looks to be:
sum_(n=0) (-4)^n

This does present a slight ambiguity in the way the question was asked. That is, if we assume that we start counting from n=0 then:
a_n = (-4)^n

However if we want to start counting from n=1 then we can write the formula as:
a_n = (-4)^(n-1)

The later formula is advantageous in that the nth term actually corresponds to that n. That is, in the first equation, the third term is at a_2 as opposed to a_3. In the second equation, the nth term is denoted simply by a_n.

Thus, it is not completely clear what the correct answer would be for a_6.

It may be:
a_6 = 4096
if we started counting from n=0

Or
a_6 = -1024
if we started counting from n = 1

We'll note that the first answer is actually the 6th term in the series, while the second is actually the 5th. If this problem were presented on homework I would most likely ask for clarification from the instructor.

Related questions
See all questions in Geometric Sequences
Impact of this question
3963 views around the world
You can reuse this answer
Creative Commons License