Question 1208674
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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).<br>
The sum of 20 terms of an AP is 20 times the average of the terms.<br>
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).<br>
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.<br>
The average of all the terms is then the average of -5 and -11/2:<br>
{{{((-5)+(-11/2))/2=(-21/2)/2=(-21/4)}}}<br>
And so the sum of the first 20 terms is {{{20(-21/4)=5(-21)=-105}}}<br>
ANSWER: -105<br>