What is the sixth term of the sequence shown in the table?
Term
Value
1
–586
2
–534
3
–482
4
–430
5
6

a₆ = 6

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = = = = -

This indicates the sequence is geometric.

To obtain any term in the sequence, multiply the previous term by r, thus

a₅ = 216 × - = - 36

a₆ = - 36 × - = 6

a₆ = 6

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = = = = -

This indicates the sequence is geometric.

To obtain any term in the sequence, multiply the previous term by r, thus

a₅ = 216 × - = - 36

a₆ = - 36 × - = 6

0.6667

162/3^(n-1)

Step-by-step explanation:

162,54,18,6,2,0.6667,etc. (the sequence is divided by 3 each time)

it is going up by 3 each time

Source:trust me bro

In the Arithmetic sequence, the common difference between consecutive terms is 3 .

The general term of an arithmetic sequence is,

where d is common difference.

Given that,  first term

So,      

Therefore, common difference is 3.

Learn more about arithmetic sequence here:

link

In the Arithmetic sequence, the common difference between consecutive terms is 3 .

The general term of an arithmetic sequence is,

where d is common difference.

Given that,  first term

So,      

Therefore, common difference is 3.

Learn more about arithmetic sequence here:

link

4th term = 28

5th term =  37

6th term = 45

Step-by-step explanation:

f(n + 1) = f(n) + 8

f(1) = 5

f(1 + 1) = f(1) + 8 = 5+8 = 13

f(2) = 13

f(2 + 1) = f(2) + 8 = 13+8 = 21

Thus, series is 5, 13, 21

In arithmetic series

Nth term is given by

n th term = a + (n-1)d

where a is the first term

and d is the common difference.

common difference d = nth term - (n-1)th term

For this series

a = 5

lets take nth term as 2nd term and 1st term as (n-1)th term

d = 13-5 = 8

n th term = a + (n-1)d

using the formula for nth term

4th term = 5 + (4-1)8 = 29

5th term = 5 + (5-1) 8= 37

6th term = 5+ (6-1)8 = 45

Thus, 4th term = 28

5th term =  37

6th term = 45

Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.

4th term = 28

5th term =  37

6th term = 45

Step-by-step explanation:

f(n + 1) = f(n) + 8

f(1) = 5

f(1 + 1) = f(1) + 8 = 5+8 = 13

f(2) = 13

f(2 + 1) = f(2) + 8 = 13+8 = 21

Thus, series is 5, 13, 21

In arithmetic series

Nth term is given by

n th term = a + (n-1)d

where a is the first term

and d is the common difference.

common difference d = nth term - (n-1)th term

For this series

a = 5

lets take nth term as 2nd term and 1st term as (n-1)th term

d = 13-5 = 8

n th term = a + (n-1)d

using the formula for nth term

4th term = 5 + (4-1)8 = 29

5th term = 5 + (5-1) 8= 37

6th term = 5+ (6-1)8 = 45

Thus, 4th term = 28

5th term =  37

6th term = 45

Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.