an > 0
a1 + (n-1)*d > 0
-97 + (n-1)*(-94-(-97)) > 0
-97 + (n-1)*3 > 0
-97 + 3n - 3 > 0
3n > 100
n > 100/3
n > 33.3 (n∈N)
n=34
Проверка: n=33; a33 = -97+32*3 = -1 < 0
n=34; a34 = -97+33*3 = +2 > 0
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an > 0
a1 + (n-1)*d > 0
-97 + (n-1)*(-94-(-97)) > 0
-97 + (n-1)*3 > 0
-97 + 3n - 3 > 0
3n > 100
n > 100/3
n > 33.3 (n∈N)
n=34
Проверка: n=33; a33 = -97+32*3 = -1 < 0
n=34; a34 = -97+33*3 = +2 > 0