SOLUTION: If the 100th term of an arithmetic sequence is 213, and its common difference is 2, then its first term a^1= a^2= a^3=

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Question 1126167: If the 100th term of an arithmetic sequence is 213, and its common difference is 2, then
its first term
a^1=
a^2=
a^3=
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

For arithmetic sequences, we use the formula
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
where a%5Bn%5D+ is the term we are trying to find, a%5B1%5D+is the first term, and d is the difference between consecutive terms, and n is the number of the term.

If the 100th term of an arithmetic sequence is a%5B100%5D=213, n=100, and its common difference is d=2, then its first term
213=a%5B1%5D%2B%28100-1%292
213=a%5B1%5D%2B%2899%292
213=a%5B1%5D%2B198
a%5B1%5D=213-198
a%5B1%5D=15

a%5B2%5D=a%5B1%5D%2B%282-1%29d
a%5B2%5D=15%2B%281%292
a%5B2%5D=17

a%5B3%5D=+19

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


A solution to the problem using the formal mathematics, as shown by the other tutor, is of course valid. But if you don't need to show a formal solution, you can get the answer with much less work.

The 1st term of the sequence is 99 terms before the 100th term, so the first term is the 100th term minus 99 times the common difference: 213-99(2) = 213-198 = 15.

Then the next two terms are found by adding 2....

ANSWERS: a(1)=15; a(2) = 17; a(3) = 19