The first term of a geometric sequence is 4 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?

2 Answers
Jim G.
Aug 4, 2018

#S_5=44#

Explanation:

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

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

#"where a is the first term and r the common ratio"#

#"here "a=4" and "r=-2#

#S_5=(4((-2)^5-1))/(-2-1)#

#color(white)(S_5)=(4(-32-1))/(-3)=(-132)/(-3)=44#

#"Alternatively"#

#"listing the first five terms of the sequence"#

#4,-8,16,-32,64#

#S_5=4-8+16-32+64=44#

maganbhai P.
Aug 4, 2018

#=S_5=44#

Explanation:

The sum of first # n # term of geometric sequence is :

#color(blue)(S_n=(a_1(1-r^n))/(1-r)#

Where , #a_1=# first term #and r=# common ratio.

We have , #a_1=4 and r=(-2)#

So, the sum of first #5 # terms is#=S_5ton=5#

#:.S_5=(4(1-(-2)^5))/(1-(-2))#

#=>S_5=(4(1-(-32)))/(1+2)#

#=>S_5=(4(1+32))/3=(4xx33)/3=4xx11#

#=>S_5=44#

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