SOLUTION: given that 6+1-4-9-...-239.Evaluate (i) the number of terms in the arithmetic sequence above.(ii) the sum of the series.

Algebra ->  Sequences-and-series -> SOLUTION: given that 6+1-4-9-...-239.Evaluate (i) the number of terms in the arithmetic sequence above.(ii) the sum of the series.      Log On


   

Question 1127068: given that 6+1-4-9-...-239.Evaluate (i) the number of terms in the arithmetic sequence above.(ii) the sum of the series.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The common difference between terms is 5 (we don't need to worry about the sign for this part of the problem).

The difference between the first and last terms, divided by the common difference, tells us how many terms there are AFTER THE FIRST ONE. So the number of terms is

(difference between first and last) divided by (common difference), PLUS 1.

%28abs%28-239-6%29%2F5%29%2B1+=+89%2B1+=+90

ANSWER (i): There are 90 terms in the sequence.

The sum of the terms is the number of terms, multiplied by the average; the average of all the terms in an arithmetic sequence is the average of the first and last terms.

average = (6-239)/2 = -233/2
number of terms = 90
sum = 90*(-233/2) = -10485

ANSWER (ii): The sum of the terms is -10485.