A5+A9=40 A7+A13=58 Найти A1; d; S100 и A100

Question

A5+A9=40
A7+A13=58
Найти A1; d; S100 и A100

Answer 1

A1+4d+a1+8d=40⇒2a1+12d=40⇒a1+6d=20
a1+6d+a1+12d=58⇒2a1+18d=58⇒a1+9d=29
отнимем
3d=9
d=3
a1=20-6*3=2
a100=a1+99d=2+297=299
S100=(a1+a100)*100/2=(2+299)*50=301*50=15050