Question 1018377
<pre>

S<sub>n</sub> = {{{n/2}}}[2a<sub>1</sub> + (n-1)d]

44 = {{{n/2}}}[2(19) + (n-1)(-3)]

44 = {{{n/2}}}[38 -3n + 3]

44 = {{{n/2}}}[41 - 3n]

88 = n[41 - 3n]

88 = 41n - 3n<sup>2</sup>

3n<sup>2</sup> - 41n + 88 = 0

(3n-8)(n-11) = 0

3n-8 = 0;  n-11 = 0
  3n = 8;     n = 11
   n = 8/3

The answer n has to be a positive integer,

so the answer is 11 terms.

Checking: 19+16+13+10+7+4+1-2-5-8-11 = 44
 
Edwin</pre>