SOLUTION: hi, I'm Sarah and i'm in 10th grade taking algebra 2, but i'm also taking an SAT prep course, and i'm having a little trouble with questions involving finding the nth term. it's qu

Question 60451: hi, I'm Sarah and i'm in 10th grade taking algebra 2, but i'm also taking an SAT prep course, and i'm having a little trouble with questions involving finding the nth term. it's quite a bit more advanced than regular math, but i hope you can still give me a hand. here is an example of one of the problems i was given:
Instructions: writs the general term of the sequence:
1,8,27,64,125,...
(answer goes here) -> Nth term:
i was also given problems using variables; but i can't understand them without first understanding how to find the answer using numerical values. i would be most appreciative if you could also work one of the questions with variables so i can get an idea of how to work them. here is a question with variables:
The sequence a, a+d, a+2d, a+3d, a+4d,... has as it's Nth or general term (answer goes in blank) -> _________
thank you in advance for your help!
Found 2 solutions by hayek, josmiceli:
Answer by hayek(51) (Show Source): You can put this solution on YOUR website!
1,8,27,64,125,...
You need to identify the relationship between the numbers. All of these numbers are perfect cubes, so the relationship is:

For the terms with variables, the relationship is already given to you:

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Look at the numbers in terms of what powers they are of what numbers

etc.
and

etc.
look at your sequence number by number
1,8,27,64,125

The first one is out of place but and also
so, the sequence is where n is the position in the sequence.
Test yourself. What is the 11th term?

what is the 10,000th term?

------------------
a, a+d, a+2d, a+3d, a+4d,...
a is the same in each term so, it's a + something
The multiplier for d looks like its position in the series minus one
n = position
answer
test this to see if it works for each term
1st term:
2nd term: etc.

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