Question 1208674
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The 10th and 15th terms of an AP are -5 and -15/2 respectively. what is the sum of the first 20 terms
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<pre>
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  {{{a[1]}}} + 9d = -5,  {{{a[1]}}} = -5 -9*(-0.5) = -5 + 4.5 = -0.5.

The 20th term is  {{{a[20]}}} = {{{a[1]}}} + 19*(-0.5) = -0.5 - 9.5 = -10.


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

    {{{S[20]}}} = {{{((a[1]+a[20])/2)*20}}} = {{{((-0.5 + (-10))/2)*20}}} = {{{(-10.5/2)*20}}} = -10.5*10 = -105.


<U>ANSWER</U>.  The sum of the first 20 terms of the AP is -105.
</pre>

Solved.