SOLUTION: -39, -44, -49, -54, ... Find a35

Question 1154055: -39, -44, -49, -54, ...
Find a35

Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

This sequence represents an arithmetic progression. Its first term is = -39. Its common difference is d = -5. The general formula for the n-th term of an arithmetic sequence is = + . In your case = -39 + (-5)*(35-1), or = -39 + (-5)*34 = -209. ANSWER

Solved.

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    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

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Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

There are 2 ways to do this kind of problem.

The first method involves listing out 35 terms, each new term is found by subtracting 5 from the previous term (eg: -39 - 5 = -44, or -44-5 = -49, and so on). This is not recommended because there are so many terms. It's easy to lose track.

A much better method is to use the general nth term formula of an arithmetic sequence. That formula is

The first term is . The common difference is since we add on -5 each time, or subtract 5 each time, to get the next term.

So,

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As a check, let's plug in a random positive integer between 1 and 4 to see if it matches up with the proper element in the sequence we're given. I'll do n = 3

Replace n with 3

The third term is -49

Sure enough, the third term of the given sequence {-39, -44, -49, -54, ...} is -49. I'll let you check the other values of n (1, 2 and 4) to see if things line up properly or not.

--------------------------------------------------------

Once we know the nth term formula, we plug in n = 35 to get the 35th term of the arithmetic sequence

Replace n with 35

The 35th term is -209

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