Question

ache os valor de n.

a) Pa ( 5,3,1,...,-25)

b) Pa ( 10,14,18,...,54)

c) Pa ( -2,-5,-8,...,-68)

d) Pa ( 1,6,11,...,76)

e) Pa ( 25,23,21,…,5)

f) Pa ( 0,7,14,...,84)

Answer 1

a)

Encontra a razão da PA

r = a2 - a1

r = 3 - 5

r = -2

an = a1 + ( n -1) . r

-25 = 5 + ( n -1) . -2

-25 = 5 - 2n + 2

-25 = 7 - 2n

-32 = -2n

n = 16

===

b)

r = a2 - a1

r = 14 - 10

r = 4

an = a1 + ( n -1) . r

54 = 10 + ( n -1) . 4

54 = 10 + 4n - 4

54 = 6 + 4n

48 = 4n

n = 12

===

c)

r = a2 - a1

r = -5 - (-2)

r = -5 + 2

r = -3

an = a1 + ( n -1) . r

-68 = -2 + ( n -1) . -3

-68 = -2 - 3n + 3

-68 = 1 - 3n

-69 = -3n

n = 23

===

d)

r = a2 - a1

r = 6 - 1

r = 5

an = a1 + ( n -1) . r

76 = 1 + ( n -1) . 5

76 = 1 + 5n - 5

76 = -4 + 5n

80 = 5n

n = 16

===

e)

r = a2 - a1

r = 23 - 25

r = -2

an = a1 + ( n -1) . r

5 = 25 + ( n -1) . -2

5 = 25 - 2n + 2

5 = 27 - 2n

-22 = -2n

n = 11

===

f)

r = a2 - a1

r = 7 - 0

r = 7

an = a1 + ( n -1) . r

84 = 0 + ( n -1) . 7

84 = 0 + 7n - 7

84 = -7 + 7n

91 = 7n

n = 13