Question

calcule a razão das seguintes progressoes aritmeticas
a) (7,10,13......) b)(18,23,28.......)

Answer 1

a)
Razão da PA ( r )
an = ak + ( n - k ) * r
7 = 10 + ( 1 - 2 ) * r
7 = 10 - 1 * r 7
- 10 = -1 * r
-3 / -1 = r 
r = 3

Razão = 3
============================
b)
Razão da PA ( r )
an = ak + ( n - k ) * r
18 = 23 + ( 1 - 2 )  *  r
18 = 23 - 1 * r
18 - 23 = -1 *  r
-5 / -1 = r
r = 5

Razão = 5

Answer 2

$r=a_2-a_1=a_3-a_2=\dots=a_{n}-a_{n-1}$

a) $(7,10,13,\dots)$

$r=a_2-a_1=10-7=3$


b) $(18,23,28,\dots)$

$r=a_2-a_1=23-18=5$