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
Algebra ->
Sequences-and-series
-> 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
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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):
