Question

calcule o numero de termos das seguintes p.g. a) (4,8,16,...,1024) r=9 b) ( 9,3,1,...,1/81)

Answer 1

a)

an = a1.$q^{n-1}$

1024 = 4.$2^{n-1}$

$2^{10} = 2^{2}.2^{n-1}$

10 = 2 + n - 1

10 - 2 + 1 = n

n = 9

b)

an = a1.$q^{n-1}$

$\frac{1}{81} = 9.\frac{1}{3}^{n-1}$

$3^{-4} = 3^{2}.{3^{-1}^{.(n-1)}$

$3^{-4} = 3^{2}.{3^{-n+1}$

-4 = 2 - n + 1

-4 - 2 - 1 = -n

-7 = -n

n = 7