Question

progressão aritmética 

Answer 1

Numero 5
$a_{n} = a_{1}+ (n-1)r$
$a_{23} = a_{1}+ (23-1)r$
$a_{23} =50$
$a_{1}= 3r$
$50= 3r+ (23-1)r$
$50 = 3r+22r \\ 50=25r$
$r=2$

Numero 6
$a_{n} = a_{1}+ (n-1)r$
$a_{10} = a_{1}+ (10-1)r$
$a_{10} =65$
$a_{1}= 2$
$a_{10} = 2+ 9r$
$65 = 2+ 9r$
$63 = 9r$
$\frac{63}{9} =r$
$r=7$
$a_{n} = 2+ 7(n-1)$

Numero 7
$a_{n} = a_{1}+ (n-1)r$
$a_{n} =-48$
$a_{1}= 8$
$-48 = 8+ (n-1)(-4)$
$-48 = 8-4n +4$
$-48-12 = -4n$
$\frac{-60}{-4}=n \\ n=15$