Answer:
The sum of the six terms is 9331
Step-by-step explanation:
* Lets explain what is the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
# [tex]U_{n}=ar^{n-1}[/tex], where a is the first term , r is the constant
ratio between each two consecutive terms, n is the position
of the term
- The sum of n terms of the geometric sequence is:
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex] , where n is the number of the terms
a is the first term and r is the common ratio
* Lets solve the problem
∵ The geometric sequence is 1 , -6 , 36 , .........
∵ The common ratio r = U2/U1
∵ U1 = 1 and U2 = -6
∴ r = -6/1 = -6
∵ The first term is 1
∴ a = 1
∵ There are 6 terms in the sequence
∴ n = 6
∴ The sum = [tex]\frac{1[1 - (-6)^{6}]}{1-6}=\frac{1[1-46656]}{-5}=\frac{-46655}{-5}=9331[/tex]
* The sum of the six terms is 9331
