The series
given is an example of arithmetic progression. The standard form of this series
is:
an = a + (<span><span>n − 1)</span> d</span>
Where,
<span>a = value of
the 1st term = 6b</span>
an = value
of the nth term
d = common
difference
n = how many
terms to add
<span>To calculate
for the common difference d, let us use the 1st term and 2nd
term. (any terms can be used as long as they are in succession)</span>
d = a2 – a1
d = 3b – 6b
d = -3b
<span>Substituting
all known value to the 1st equation:</span>
an = 6b
+ (<span><span>n − 1)</span> (-3b)</span>
an = 6b -3bn +3b
an = -3bn + 9b
Since there are only 5
terms therefore n = 1 to 5. The sigma notation is:
<span>D. sigma,
n=1, 5 above the sigma, -3bn+9b</span>
