1. d=-3; an=-15; Sn=-36
an=a1+d(n-1)
a1–3n+3=-15
a1=3n-18
2a1–3n+3 2(3n–18)–3n+3
Sn = --------------- • n = ---------------------
2 2
6n–36–3n+3 3n–33
•n = ------------------- • n = ---------- • n =
2 2
3(n–11)
= ---------- • n = 1,5(n–11)•n
2
1,5n(n–11)=–36
1,5n^2–16,5n+36=0
Д=/272,25–4•1,5•36=/56,25=7,5
n1=(16,5+7,5)/3=8
n2=(16,5–7,5)/3=3
При n=3:
a1=3•3–18=–9
При n=8:
a1=3•8–18=6
2. d=3; an=23; Sn=85
an=a1+3n–3
a1+3n–3=23
a1=26–3n
2a1+3n–3 2(26–3n)+3n–3
Sn = --------------- • n = ----------------------
2 2
52–6n+3n–3 49–3n
• n = ------------------- • n = ---------- • n
2 2
(49–3n)•n=170
49n–3n^2–170=0
Д=/2401–4•(-3)•(-170)=/361=19
n1=(–49+19)/(-6)=5
n2=(–49–19)/(–6)=-68/(-6)=11 1/3 не может являться решением.
a1=26–3•5=11