12.4. Arithmetic Series http://www.ck12.org
- Evaluate the following sum.
500
i∑= 02 i−^312
Answers: - The initial term is -1 and the common difference is^53.
n
i∑= 1 ai=n
2 (^2 a^1 +(n−^1 )k)
=^152(
2 (− 1 )+( 15 − 1 )^53
)
=^152
(
− 2 + 14 ·^53
)
= 160
- The initial term is -7 and the common difference is 3.
n
∑i= 1 ai=n
2 (^2 a^1 +(n−^1 )k)
=^1002 ( 2 (− 7 )+( 100 − 1 ) 3 )
= 14150- The initial term is -312 and the common difference is 2.
500
i∑= 02 i−^312 =501
2 (^2 (−^312 )+(^501 −^1 )^2 )
= 94188
Practice
Sum the first 24 terms of the sequence 1, 5 , 9 , 13 ,...
Sum the first 102 terms of the sequence 7, 9 , 11 , 13 ,...
Sum the first 85 terms of the sequence− 3 ,− 1 , 1 , 3 ,...
Sum the first 97 terms of the sequence^13 ,^23 , 1 ,^43 ,...
Sum the first 56 terms of the sequence−^23 ,^13 ,^43 ,...
Sum the first 91 terms of the sequence− 8 ,− 4 , 0 , 4 ,...
Evaluate the following sums.
300
i∑= 03 i+^18215
i∑= 05 i+^1