a1 = 6
r = 2
an = a1(r^(n-1))
an = 6(2^(n-1))
a1 = 6x2^0 = 6
a2 = 6x2^1 = 12
a3 = 6x2^2 = 24
a4 = 6x2^3 =48
a5 = 6x2^4 =96
a6 = 6 x32 = 192
...
an = 6 x 2^(n-1)
...
a10 = 6x 2^9 = 3072
...
each term is double the previous term
the nth term = an = 2(an-1)
1st 6 terms are:
a1,a2,a3,a4,a5,a6,...
= 6,12,24,48,96, 192, ...
the nth term = 6 times (2 raised to the n-1 power)
the graph is an exponential curve
with n measured on the x axis, the horizontal axis
and a measured on the y axis, vertical axis
the curve has a y intercept = 6 = a1 = the point (0,6)
the curve has a horizontal asymptote y=0
to the left, as n approaches negative infinity, a approaches zero
to the right, as n approaches infinity, a approaches infinity
no points in the graph are in quadrants III or IV
all points are in quadrants I and II
for n>1, all points are in quadrant I
for n<1 all points are in quadrant II
for n=1 the point is on the y axis, the border between quadrant I and II
an is always >0
