Question

Express the series using sigma notation 6b + 3b + 0 + (-3b) + (-6b).

CHOICES:
A. sigma n=1 5 above the sigma, -3bn-9b
B. sigma n=1, infinity above the sigma, -3bn+9b
C. sigma, n=1, infinity above the sigma, -3bn-9b
D. sigma, n=1, 5 above the sigma, -3bn+9b

Answer 1

The series given is an example of arithmetic progression. The standard form of this series is:

an = a + (n − 1) d

Where,

a = value of the 1st term = 6b

an = value of the nth term

d = common difference

n = how many terms to add

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)

d = a2 – a1

d = 3b – 6b

d = -3b

Substituting all known value to the 1st equation:

an = 6b + (n − 1) (-3b)

an = 6b -3bn +3b

an = -3bn + 9b

Since there are only 5 terms therefore n = 1 to 5. The sigma notation is:

D. sigma, n=1, 5 above the sigma, -3bn+9b