SOLUTION: Find the nth term for this increasing arithmetic sequence: 2,4,6,8,10...

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Question 1201812: Find the nth term for this increasing arithmetic sequence:
2,4,6,8,10...
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


ANSWER: 2n

The common difference is 2, so the formula for the n-th term is 2n+a for some number a.

When n=1, the term is 2, so

2(1)+a = 2
2+a = 2
a = 0

So the formula for the n-th term is 2n+0, or just 2n.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: a%5Bn%5D+=+2n

Explanation:
n = a positive integer
a1 = 2 is the first term
d = 2 is the common difference, the gap between terms
a%5Bn%5D+=+matrix%281%2C2%2Cnth%2Cterm%29

a%5Bn%5D+=+a%5B1%5D%2Bd%28n-1%29

a%5Bn%5D+=+2%2B2%28n-1%29

a%5Bn%5D+=+2+%2B+2n+-+2

a%5Bn%5D+=+2n

As a check, let's plug in say n = 3
a%5Bn%5D+=+2n

a%5B3%5D+=+2%2A3

a%5B3%5D+=+6
The third term is indeed 6. I'll let you check the other values of n.
n = 1, 2, 3, ...