Question

interpole e dê a PA:

(A) Cinco meios aritméticos entre 3 e 13

(B) sete meios aritméticos entre 5 e 11

Calcule a soma:

(A) dos vinte primeiros termos da PA (3,7...)

(B) De todos os Termos da PA (4,1,...,-38)

Answer 1

a)

3,a2,a3,a4,a5,a6,13

a7= a1+6r
13= 3+6r
13-3= 6r
10=6r
r= 10/6
r= 5/3

3_5
--+--- =
1__3

9+5
------
_3

14/3

3,14/3,19/3,21/3,26/3,29/3

(3,14/3,19/3,7,26/3,13)

b)

5,a2,a3,a4,a5,a6,a7,a8,11

a9= a1+8r
11= 5+8r
11-5= 8r
6= 8r
r= 6/8
r= 3/4

5__3
---+----
1___4

20+3
--------
__4

23/4

(5,23/4,26/4,29/4,32/4,35/4,38/4,41/4,44/4)

5,23/4,26/4,29/4,8,35/4,38/4,41/4,11)

calcule a soma

a)
(3,7.....)

Sn= (a1+an).n
____------------
_______2

Sn= (3+an).20
____------------
_______2

Sn= (3+79).20
____-----------
_______2

Sn= 82.20
___--------
_____2

Sn= 820

r= a2-a1
r= 7-3
r= 4

an= a1+(n-1).r
an= 3+(20-1).4
an= 3+(19).4
an= 3+76
an= 79

b)

(4,1,........,-38)

an= a1+(n-1).r

-38= 4+(n-1).(-3)
-38= 4+(-3n+3)
-38= 4-3n+3
3n= 38+7
3n= 45
n= 45/3
n= 15

r= a2-a1
r= 1-4
r= -3

Sn= (a1+an).n
___-------------
______2

Sn= (4+(-43)).15
___---------------
_______2

Sn= (4-43).15
___------------
______2

Sn= -39.15
___----------
_____2

Sn= 292,5