в арифметической прогрессии найти S40, если S10=100, а S30=900

s10=100,s30=900,s40=?sn=n/2(a1+an)s10=5(a1+a10), 100=5(a1+a10), a1+a10=20s30=15(a1+a30), 900=15(a1+a30), a1+a30=60a1+a10=20,a1+a1+9d=20,2a1+9d=20a1+a30=60, a1+a1+29d=60,2a1+29d=60---2a1+9d=202a1+29d=60-----20-9d=60-29d, 20d=40,d=22a1=20-9d,2a1=20-18,2a1=2,a1=1a40=a1+39d,a40=1+39.2=1+78,a40=79s40=40/2(1+79)=20.80=1600s40=1600