Question

Dau coroana pentru ambele ex rezolvate corect si intregi!

Answer 1

Răspuns:

Explicație pas cu pas:

23.

a1 = 2

a3 = 8

S30 = ?

an = a1 + (n - 1)*r

Sn = 2*(a1 + an)/2

a3 = a1 + 2r

8 = 2 + 2r

6 = 2r

r = 3

a30 = a1 + 29r = 2 + 29*3 = 89

S30 = 30*(2 + 89)/2 = 30*91/2 = 1365

__________

24.

a1 = 2013

r = -2

a2016 = ?

n = 2016

an = a1 + (n - 1)*r

a2016 = 2013 + 2015*(-2) = 2013 - 4030 = -2017

Answer 2

$\displaystyle 23.~~a_1=2,~a_3=8,~S_{30}=?\\\\a_n=a_1+(n-1)\cdot r\\\\ a_3=8 \Rightarrow a_1+(3-1)\cdot r=8\Rightarrow 2+2r=8 \Rightarrow 2r=8-2 \Rightarrow 2r=6\Rightarrow \\\\r=\frac{6}{2} \Rightarrow r=3\\\\ S_n=\frac{n[2a_1+(n-1)\cdot r]}{2} \\\\ S_{30}=\frac{30[2 \cdot 2+(30-1)\cdot 3]}{2} =\frac{30(4+29 \cdot 3)}{2} =\frac{30 (4+87)}{2} =\frac{30 \cdot 91}{2} =\\\\ =\frac{2730}{2} =1365$

$24.~~a_1=2013,~r=-2,~a_{2016}=?\\\\a_n=a_1+(n-1)\cdot r\\\\ a_{2016}=a_1+(2016-1)\cdot r=2013+2015 \cdot (-2)=2013-4030=-2017$