What is the sum of the geometric sequence 1,-6,36 if there are 6 terms

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

# , 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:

  , 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 =

* The sum of the six terms is 9331

step-by-step explanation: