Question

How can I find the answer for number 1 and 4 with explanation?​

Answer 1

Concept: Sequences & Series

The hint here is to try to find the common factor, you asked us to solve 1 so see the solution below.

1. 1,-3,9, -27 : We see a common base of 3 hence we can find that the series representation is
2. 
   `( - 3) ^(n-1)`

Next we can find the next 3 terms by just plugging in the values

We want the 6th, 7th, and 8th term

So we plug 6 in for n and 7 in for n and 8 in for n

So we get the 6th term=-243

The 7th term= 729

The 8th term= -2187

Answer 2

Explanation:

1) 1 , -3 , 9 , -27 , 81 ,...........

It is Geometric sequence

ratio = 2 term ÷ first term = -3 ÷ 1 = -3

1st term = 1

2nd term = 1 * -3 = -3

3rd term = -3 *(-3) = 9

4th term = 9 *(-3) = - 27

6th term = 81 *(-3) = -243

7th term = -243 *(-3) = 729

8th term = 729 *(-3) = -2187

Next 3 terms: - 243 , 729 , - 2187,....

4)

`(1)/(2), (1)/(2) , (3)/(8) , (1)/(4) ,(5)/(32),.....\\\\\\Rule = (n)/(2^(n))\\Term1 = (1)/(2^(1))=(1)/(2)\\\\Term2 = (2)/(2^(2))=(2)/(4)=(1)/(2)\\\\Term3 = (3)/(2^(3))=(3)/(8)\\\\Term4 = (4)/(2^(4))=(4)/(16)=(1)/(4)\\\\Temr5 = (5)/(2^(5))=(5)/(32)\\\\Term6 = (6)/(2^(6)) = (6)/(64) = (3)/(32)\\\\Term7 = (7)/(2^(7))=(7)/(128)\\\\Term8 =(8)/(2^(8)) = (8)/(256)=(1)/(32)\\\\`

Next 3 terms are : 3/32 , 7/128 , 1/32