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
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(rn−1)r−1
"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)5−1)−2−1
color(white)(S_5)=(4(-32-1))/(-3)=(-132)/(-3)=44S5=4(−32−1)−3=−132−3=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=4−8+16−32+64=44
Explanation:
The sum of first
color(blue)(S_n=(a_1(1-r^n))/(1-r)Sn=a1(1−rn)1−r
Where ,
We have ,
So, the sum of first