Question 1177107: consider the sequence of numbers: 2;5;2;9;2;13;2;17
calculate the sum of the first 100 terms of the sequence
Found 2 solutions by mccravyedwin, MathLover1:
Answer by mccravyedwin(407)   (Show Source):
You can put this solution on YOUR website!
2,5,2,9,2,13,2,17,...
The sum of the 50 odd numbered terms
2,_,2,_,2,_,2,_,...2
is 50*2 = 100 <--sum of odd numbered terms (all 2's)
-------------------------
The sum of the 50 even-numbered terms:
5,__,9,__,13,__,17,__,...
That's 50 terms of an arithmetic sequence with common difference 4:
 <--sum of even-numbered terms.
------------------
Add them together = 100 + 5150 = 5250 <--answer
Edwin
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!  , ,, ,, ,, ,...
pattern:
all odd number terms are equal,
in  terms you have  of them; so their sum is 
all even number terms, you also have of them, have common difference  ;
and so on, and the formula for nth term of an arithmetic progression is
 where  and 
so.
sum of all even number terms is:
add both odd and even terms sums
 ->the sum of the first terms
|
|
|
