Question

Найти первый член арифметической прогрессии сn, если: а) с9=17; d=2; б)c4=7; c9=-8.

Answer 1

a) с₉ = 17     d = 2      c₁ = ?

c₉ = c₁ + 8d

c₁ = c₉ - 8d = 17 - 8 * 2 = 17 - 16 = 1

б) c₄ = 7       c₉ = - 8      c₁ = ?

$\left \{ {{c_{9}=-8 } \atop {c_{4}=7 }} \right.\\\\-\left \{ {{c_{1} +8d=-8} \atop {c_{1}+3d=7 }} \right.\\ -------\\\\5d=-15\\\\d=-3$

c₁ = 7 - 3d = 7 - 3 * (- 3) = 7 + 9 = 16