Question

НАЙДИТЕ а1 и d если в арифметическое прогрессии а3=-5 а15=59

Answer 1

$a_n=a_1+(n-1)d$

$\left \{ {{a_3=-5} \atop {a_{15}=59}} \right. \\\\ \left \{ {{a_1+2d=-5} \atop {a_1+14d=59}} \right. \\\\ \left \{ {{a_1=-2d-5} \atop {-2d-5+14d=59}} \right. \\\\ \left \{ {{a_1=-2d-5} \atop {12d=64}} \right. \\\\ \left \{ {{a_1=-2d-5} \atop {d=\frac{64}{12}=\frac{16}{3}}} \right. \\\\ \left \{ {{a_1=-2*\frac{16}{3}-5=-\frac{32+15}{3}=-\frac{47}{3}} \atop {d=\frac{16}{3}}} \right. \\\\ \left \{ {{a_1=-\frac{47}{3}} \atop {d=\frac{16}{3}}} \right.$