Question

Calcule a fórmula do termo geral de cada PA:

a) (2,7,...) b) -1,5,...) c) (p -2, p,...)

Answer 1

a) Primeiro descobrimos a razão r = a2-a1 r=7-2=5
An= a1 + (n-1) x r
A5= 2 + (5-1) x 5
A5= 2 + 4 x 5
A5= 2 + 20
A5= 22

Answer 2

Termo geral
a)
(2,7,...)

$a_1=2 \\ n=n \\ r=7-2=5 \\ \\ a_n=a_1+(n-1)r \\ \\ a_n=2+(n-1)5 \\ \\ a_n=2+5n-5 \\ \\ a_n=5n-3~~~(termo~~geral)$

b)
$a_1=-1 \\ n=n \\ r=5-(-1)=5+1=6 \\ \\ a_n=a_1+(n-1)r \\ \\ a_n=-1+(n-1)6 \\ \\ a_n=-1+6n-6 \\ \\ a_n=6n-7~~~~(termo~~~geral)$

c)
$a_1=p-2 \\ n=n \\ r=p-(p-2)=\not p-\not p+2=2 \\ \\ a_n=a_1+(n-1)r \\ \\ a_n=p-2+(n-1)2 \\ \\ a_n=p-2+2n-2 \\ \\ a_n=p+2n-4~~~~(termo~~~geral)$