Question

Арифметическая прогрессия an a 6 = a 10 = найти s6?

Answer 1

Если A6=3/4, а A10=1 3/4, то d=1/4
d=(An-A1)/(n-1)
1/4=(3/4-A1)/(6-1)
A1=4/5

Sn=((A1+An)*n)/2
S6=((4/5+3/4)*6)/2=4.65

Answer 2

$a_n=a_1+(n-1)d;\\ a_6=a_1+5d;\\ a_{10}=a_1+9d;\\ a_{10}-a_6=a_1+9d-a_1-5d=4d;\\ a_{10}=a_6+4d;\\ 4d=a_{10}-a_6=1\frac34-\frac34=1;\\ d=\frac14;\\ a_6=a_1+5d;\\ a_1=a_6-5d=\frac34-5\cdot\frac14=\frac34-\frac54=-\frac24=-\frac12;\\ S_6=\frac{a_1+a_6}{2}\cdot n=\frac{-\frac24+\frac34}{2}\cdot6=\frac14\cdot3=\frac34;\\$