SOLUTION: sum the serie: 1+5+9+...+77

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Question 945364: sum the serie: 1+5+9+...+77
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
General term of the sequence, 1%2B4%28n-1%29 for index n.
Which index is the term, 77?
1%2B4%28n-1%29=77
1%2B4n-4=77
4n=77%2B4-1
4n=80
highlight_green%28n=20%29

You can avoid dealing with the formula for sum of a sequence if you use simple sense and understanding about arithmetic series.

You have twenty terms. you can form ten pair of sums all equivalent to FirstTerm%2BLastTerm, or 1%2B77=78. No term is unpaired because you have n=20, an EVEN number of terms. The sum is 78, occurring in a sum 10 times.

highlight%2810%2A78=highlight%28780%29%29