Question

Calcule
a) 1+2+3+...+70 =
b) -33-28-23-...+38 =
c) 28+33+38+...+108 =
d) 22+18+14+...-38 =​

Answer 1

Resposta:

Explicação passo-a-passo:

a) 1+2+3+...+70 =

an = 70

a1 = 1

r = a2-a1

r = 2-1

r = 1

An = a1+(n-1).r

70 = 1 + (n-1).1

70 = 1 + n - 1

70 = n

n = 70

Sn = (a1+an).n/2

S70 = (1+70).70/2

S70 = 71.35

S70 = 2485

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b) -33; -28; -23; - 18; - 13; - 8; - 3; 2; 7...+37 =

r = a2-a1

r = -28-(-33)

r = - 28 + 33

r = 33 - 28

r = 5

an = a1+ (n-1).r

37 = - 33 + (n -1).5

37= 5n - 5 - 33

37 = 5n - 38

37+38= 5n

75 = 5n

5n = 75

N = 15

Sn = (a1+an).n/2

S15 = (-33+37).15/2

S15 = 4.15/2

S15 = 30

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c) 28+33+38+...+108 =

R = a2 - a1

R = 33 - 28

R = 5

an = a1 + (n-1).r

108 = 28 + (n-1).5

108 = 28 + 5n - 5

108 = 23 + 5n

108 - 23 = 5n

85 = 5n

5n = 85

n = 85/5

n = 17

S17 = (a1+ a17).17/2

S17 = (28+108).17/2

S17 = 136/2 . 17

S17 = 68.17

S17 = 1156

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d) 22+18+14+...-38 =​

r = a2 - a1

r = 18 - 22

r = - 4

an = a1 + (n-1).r

- 38 = 22 + (n-1).(-4)

- 38 - 22 = - 4n + 4

- 60 - 4 = - 4n

- 64 = - 4n (-1)

64 = 4n

4n = 64

N = 16

Sn = (a1+an).n/2

S16 = (22 - 38).16/2

S16 = - 16.8

S16 = - 128