Question

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

Answer 1

Answer:

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

Answer:

Step-by-step 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)

$\frac{1}{2}, \frac{1}{2} , \frac{3}{8} , \frac{1}{4} ,\frac{5}{32},.....\\\\\\Rule = \frac{n}{2^{n}}\\Term1 = \frac{1}{2^{1}}=\frac{1}{2}\\\\Term2 = \frac{2}{2^{2}}=\frac{2}{4}=\frac{1}{2}\\\\Term3 = \frac{3}{2^{3}}=\frac{3}{8}\\\\Term4 = \frac{4}{2^{4}}=\frac{4}{16}=\frac{1}{4}\\\\Temr5 = \frac{5}{2^{5}}=\frac{5}{32}\\\\Term6 = \frac{6}{2^{6}} = \frac{6}{64} = \frac{3}{32}\\\\Term7 = \frac{7}{2^{7}}=\frac{7}{128}\\\\Term8 =\frac{8}{2^{8}} = \frac{8}{256}=\frac{1}{32}$

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