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
Aug 4, 2018

S_5=44S5=44

Explanation:

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

•color(white)(x)S_n=(a(r^n-1))/(r-1)xSn=a(rn1)r1

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

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

S_5=(4((-2)^5-1))/(-2-1)S5=4((2)51)21

color(white)(S_5)=(4(-32-1))/(-3)=(-132)/(-3)=44S5=4(321)3=1323=44

"Alternatively"Alternatively

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

4,-8,16,-32,644,8,16,32,64

S_5=4-8+16-32+64=44S5=48+1632+64=44

Aug 4, 2018

=S_5=44=S5=44

Explanation:

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

color(blue)(S_n=(a_1(1-r^n))/(1-r)Sn=a1(1rn)1r

Where , a_1=a1= first term and r=andr= common ratio.

We have , a_1=4 and r=(-2)a1=4andr=(2)

So, the sum of first 5 5 terms is=S_5ton=5=S5n=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