Question

Progresie aritmetică, r=3, a673=2020. Arătați că S9=a1².​

Answer 1

Răspuns:

FALS

Explicație pas cu pas:

a1=a673-672r=2020-672*3=4

S9=a1+a2+..+a8=a1(1+r+....+r^7) =a1(r^8-1)/(r-1)=4(3^8-1)/(3-1)=2(81²-1)

a1²=4²=16

2(81²-1)=16

81²-1=8

81²=9

fals

Answer 2

$\it a_1=a_{673}-672\cdot r = 2020 - 672\cdot3= 2020 - 2016 = 4\\ \\ a_9 = a_1+8r = 4+8\cdot3 = 28\\ \\ S_9=\dfrac{(a_1+a_9)\cdot9}{2}=\dfrac{(4+28)\cdot9}{2} =\dfrac{32\cdot9}{2} =16\cdot9=9\cdot16=9\cdot a_1^2$