Question 429014: Hi, my son and I are having trouble figuring out his homework on "series and sequences". I don't know about you but I have never heard of that. Anyway these are the three problems:
1. Find the sum of the 1st 20 terms of the sequence 7,13,19...
2. Write the sum of the 1st n terms of the sequence -5,-2,1,...
3. How many terms of the sequence -19,-15,-11,... must be taken to give a sum of 98?
Thank you for your time and consideration! Your help is greatly appreciated.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! A sequence is a collection of terms or objects in some order. For example, {4,7,10,13,...}, {6.4, pi, 8, -5,...} and {cat,dog,chicken,horse,...} can be considered sequences. A series is defined as the sum of the terms in a sequence.
For those three questions, use the formula  where n is the number of terms in the arithmetic sequence,  is the sum of the first n terms,  is the first term, and  is the n-th term. I rarely see students try to memorize the formula, since it is often easier to re-derive it instead of memorize it (being able to derive the formula is also more advantageous than memorizing).
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