若a6 a9 a12 a15=20,则S20=?

是等差数列

热心网友

{an}是等差数列，若a6+a9+a12+a15=20,则S20=?解：a6+a9+a12+a15=20a1+5d+a1+8d+a1+11d+a1+14d=204a1+38d=202a1+19d=10所以S20=20a1+[20(20-1)d/2]=20a1+190d=10(2a1+19d)=10×10=100

热心网友

a6 + a9 + a12 + a15 = 20== (a1+5d)+(a1+9d)+(a1+11d)+(a1+14d) = 20== 2*a1 + 19d = 10S20 = (a1+a20)*20/2 = 10*[a1 + (a1+19d)] = 10*(10) = 100