Question #b6ffe

2 Answers
Jul 28, 2017

Two ways

Explanation:

We observe that these are the first few terms of a geometric sequence because the ratio of each term to the term before it is the same value ... -3.

For this sum,
the first term is #a_0 = 1#.
The common ratio is #r = -3#.
Since #-243 = (-3)^5#, there are six terms altogether.

By the formula for summation
#S_5 = (1-r^6)/(1 - r)#
#S_5 = (1-(-3)^6)/(1 - (-3))#
#S_5 = (1-729)/(1 +3)#
#S_5 = -728/4#
#S_5 = -182#

For this particular sum, we have

#1 - 3 + 9 - 27 + 81 - 243#.

Add these up to get #-182#.

Jul 28, 2017

#-182#

Explanation:

#"the sum to n terms of a geometric series is"#

#•color(white)(x)S_n=(a(1-r^n))/(1-r)#

#"where a is the first term, r the common ratio and n the"#
#"number of terms"#

#"here " a=1, r=(-3)/1=9/(-3)=-3 ,n=6#

#rArrS_6=(1(1-(-3)^6))/(1-(-3)#

#color(white)(rArrS_6)=(1-729)/4=-182#