SOLUTION: An arithmetic sequence has 1st term 6 and common difference 624. A geometric sequence has 1st term 2 and common ratio 3. Determine an n so the nth term of the arithmetic sequen

Question 982910: An arithmetic sequence has 1st term 6 and common difference 624. A geometric sequence has 1st term 2 and common ratio 3. Determine an n so the nth term of the arithmetic sequence is the same as the nth term of the geometric sequence.
I set this up as:
a(n) = 6 + (n-1)*624
a(n) = 2*3^(n-1)
I set these equal to each other and basically guess and check. When I do this I get a value of 8.
However, I have seen this done a different way that looks like this:
a(n) = 6 + 624n
a(n) = 2*3^n
3 + 312n = 3^n
For this I get a value of 7.
Is the general equation to find a value of n only supposed to be n and not the n-1 that I was using?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Both ways are correct. If you start counting at n = 1, then for a(1) to equal 6, you have to have 6 + (1 - 1)*624 and for a(1) to equal 2 for the geometric series, you have to have 2 * 3^(1-1).

But if you start your count at n = 0, the arithmetic series first term is 6 + 624*0 = 6, and the geometric is 2*3^0 = 2.

In the first case, 1 to 8 is 8 terms. In the second case, 0 to 7 is 8 terms.

John

My calculator said it, I believe it, that settles it

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