SOLUTION: Consider the sequence of numbeer: 2;5;2;9;2;13;2;17 Calculate the sum of the first 100 terms of the sequence

Question 1152869: Consider the sequence of numbeer: 2;5;2;9;2;13;2;17
Calculate the sum of the first 100 terms of the sequence
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

ASSUMING THAT THE APPARENT PATTERN CONTINUES....

The sequence can be viewed as two spliced sequences each of 50 terms:

   2   2   2   2   ...   2   2   2
      5   9  13           197 201

One method for finding the sum would be to calculate the sum of each of these sequences separately. But perhaps a faster path to the solution is to group the 100 terms into pairs, obtaining a sequence of 50 terms:

   7  11  15  ...  199 203

The sum is then

(number of terms) times (average of all the terms)

which is equivalent to

(number of terms) times (average of first and last terms):

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