Question

Urgent fisa lucru matematica

Answer 1

Răspuns:

Explicație pas cu pas:

1)

a1=2

r=3

a4=a1+3*r=2+6=8

2) 2(x+5)=x-1+2x+8  adica termenul din mijloc este media aritmetica a termenilor vecini

2x+10=3x+7

x=3

3) a) 1+5+9+13+17+21+25=91

b)

a7=17

a8=25

a7=a1+6r=17

a8=a1+7r=25

25=a1+7r

17=a1+6r

scad cele 2 relatii

r=8

a1=17-48=-31

c)

a1=-5

r=2,3

a11=a1+10r=-5+23=18

Answer 2

Explicație pas cu pas:

progresie aritmetică:

$\boxed {a_{n} = a_{1} + (n - 1)\cdot r}$

1)

$a_{1} = 2; \ r = 3; \ n = 4$

$a_{4} = 2 + (4 - 1) \cdot 3 = 2 + 3 \cdot 3 = 2 + 9 = \bf 11$

2)

$2(x + 5) = (x - 1) + (2x + 8)$

$2x + 10 = x - 1 + 2x + 8$

$\implies \bf x = 3$

3)

$\boxed {a_{n + 1} - a_{n} = r}$

5 - 1 = 4; 9 - 5 = 4 => r = 4

$\boxed {n = (a_{n + 1} - a_{n}) : r + 1}$

n = (25 - 1 ) : 4 + 1 => n = 7

$\boxed {S_{n} = \dfrac{(a_{1} + a_{n})\cdot n}{2}}$

$a_{1} = 1; \ a_{n} = 25; \ n = 7$

$S_{7} = 1 + 5 + 9 + ... + 25 = \dfrac{(1 + 25)\cdot 7}{2} = \dfrac{26\cdot 7}{2} = \bf 91$

4)

$r = a_{8} - a_{7} = 25 - 17 \implies \bf r = 8$

$a_{7} = a_{1} + (7 - 1)\cdot 8 \\ a_{1} = 17 - 48 = - 31 \\ \implies \bf a_{1} = - 31$

5)

$a_{1} = - 5 \ ; \ r = 2,3 \ ; \ n = 11$

$a_{11} = - 5 + (11 - 1)\cdot 2.3 = - 5 + 10\cdot 2.3 = - 5 + 23 = \bf 18$