Question

Quantos elementos tem a PG (8,32,...12)?

Answer 1

a1 = 8
a2 = 32
an = 12
.
r = 32/8 = 4
.
an = a1•r^(n-1)
.
12 = 8•4^(n-1)
.
12 = 2³•2^(2n-2)
.
12 = 2^(3 + 2n -2)
.
12 = 2^(2n +1)
.
12 = 2•2²ⁿ
.
12/2 = 2²ⁿ
.
6 = 2²ⁿ
.
2n = log6 na base 2
.
n = [log6 na base 2]/ 6
.