SOLUTION: The 10th and 15th terms of an AP are -5 and -15/2 respectively.what is the sum of the first 20 terms

Algebra.Com
Question 1208674: The 10th and 15th terms of an AP are -5 and -15/2 respectively.what is the sum of the first 20 terms
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The difference between the 10th and 15th terms is (-15/2)-(-5) = (-15/2)+(10/2) = -5/2, so the common difference is (-5/2)/5 = (-1/2).

The sum of 20 terms of an AP is 20 times the average of the terms.

In an AP with an even number of terms, the average of all the terms is the average of the two middle terms (10th and 11th terms).

We were given that the 10th term is -5, and we determined that the common difference is -1/2, so the 11th term is -5-1/2 = -11/2.

The average of all the terms is then the average of -5 and -11/2:



And so the sum of the first 20 terms is

ANSWER: -105
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
The 10th and 15th terms of an AP are -5 and -15/2 respectively. what is the sum of the first 20 terms
~~~~~~~~~~~~~~~~~~~~ 

The 10th term is -5;  the 15th term is -15/2 = -7.5.

The difference between the 15th term and the 10th term is -7.5 - (-5) = -7.5 + 5 = -2.5.

Between the 10th term and 15th term, there are 5 equal gaps, each equal to the common difference d.
so, the common difference d = -2.5/5 = -0.5.


The 10th term is -5,  so   + 9d = -5,   = -5 -9*(-0.5) = -5 + 4.5 = -0.5.

The 20th term is   =  + 19*(-0.5) = -0.5 - 9.5 = -10.


Thus the sum of the first 20 terms of the AP is

     =  =  =  = -10.5*10 = -105.


ANSWER.  The sum of the first 20 terms of the AP is -105.

Solved.



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