Question

2º) Dada a P.A (3,5,7...) Encontre:

a) a21

b) S21

3º) Dada a P.G (3,6,12...) Encontre:

a) a21

b) s21

Answer 1

2°)
a) Dados:
a₁=3
r=7-5=2
n=21

An=a₁+(n-1)*r
a₂₁=3+(21-1)*2
a₂₁=3+20*2
a₂₁=3+40
a₂₁=43


b)
$Sn= \frac{n(a_{1} +an)}{2} \\ \\ S _{21} =\frac{21(3 +43)}{2} \\ \\ S _{21} =\frac{21(46)}{2} \\ \\ S _{21} =\frac{966}{2} \\ \\ S _{21} =483$


3°)
a) Dados:
a₁=3
q=$\frac{12}{6} =2$

$An=a _{1} *q ^{n-1} \\ \\ a _{21} =3*2 ^{21-1} \\ \\ a _{21} =3*2 ^{20} \\ \\ a _{21} =3*1048576 \\ \\ a _{21} =3145728$


b)
$Sn= \frac{a_{1}(q ^{n}-1) }{q-1} \\ \\ S _{21} = \frac{3(2^{21}-1) }{2-1} \\ \\ S _{21} = \frac{3(2097152-1) }{1} \\ \\ S _{21} = 3(2097151) \\ \\ S _{21} = 6291453$