Question

quantos termos tem a seguinte PG (7,14,28,...,3584)

Answer 1

a1 = 7
>>>>>>>>
a2 = 14
>>>>>>>>
q = a2
......___
.......a1

q = 14
.....___
.......7

q = 2
>>>>>>>>>
an = 3.584


1er paso vamos utilizar a formula general:

an = a1 x q^(n-1)

3.584 = 7 x 2^(n-1)

7 x 2^(n-1) = 3.584

2^(n-1) = 3.584
..............._____
....................2

2^(n-1) = 512

2^(n-1) = 2^9

n-1 = 9

n = 9 + 1

n = 10

2do paso vamos fazer a formula da soma de dos termos sao :

Sn = a1 x (q^n-1)
........_________
..............(q - 1)

S10 = 7 x (2^10 - 1)
..........___________
...................(2-1)

S10 = 7 x (1.024 - 1)
..........___________
.......................1

S10 = 7 x 1.023

S10 = 7161