Question

PLEASE HELP ME ASAP!!!!!!!!!!!!!!!!!

Use the sequence 10,−2, 2/5, −2/25,… for questions 4-6
.
4. Find the next three terms in the sequence.

5. Find an equation that defines the ak term of the sequence.

6. Find the 12th term of the sequence.

Answer 1

4.

5th term = -(2/25 x -5) = 2/125

6th term = -2/(125 x - 5) = -2/625

7th term = 2/(625 x-5) = 2/3125

5.

`a_k = 10 ((-1)/(5) )^(k-1)`

6 .

`a_(12) = 10 (-(1)/(5) ) ^ {11} = -(10)/(48828125)`

Explanation:

This is a geometric sequence with the common ratio 1/5 and sign that changes every alternate term. We can also state that the common ratio is -
`(1)/(5)`

First term is 10 with +ve sign

Second term is 10/5 with negative sign = -2

Third term is -2/5 with positive sign = 2/5

Fourth term is 2/5 ÷ 5 = 2/25 with negative sign = -2/25

4. Since each subsequent term = (-1/5) x (previous term) we have

5th term = -(2/25 x -5) = 2/125

6th term = -2/(125 x - 5) = -2/625

7th term = 2/(625 x-5) = 2/3125

5. General equation

Let
`a_k` be the kth term

Since this is a geometric sequence, the general equation is

`a_k = a_1r^(k-1)`

`\text{where } a_1 \text { is the first term and r is the common ratio}`

so the equation is

`a_k = 10 ((-1)/(5) )^(k-1)`

6. The 12 term is calculated as

`a_(12) = 10 (-(1)/(5) ) ^ {11} = -(10)/(48828125)`

Answer 2

Explanation: