Circle the appropriate category for each of the following se

Circle the appropriate category for each of the following sequences (airthmetic, geometric, or neither). neither). Give the common differences or common ratio, or circle \"not applicable.\" Find the tenth term (use applicable formulas). 1. 1, -1, 1, -1,... 2. 1, 1, 2, 3, 5, 8, 13,... 3. 11, 9, 7, 5,...

Solution

Answer 1.

1 , -1, 1 , -1....

See each term is multiplied with -1 every time then it becomes next term.

So this is geometric sequence which has common ratio -1.

So, the sequence is 1, -1, 1, -1, 1, -1, 1, -1, 1, -1

Answer 2.

1,1,2,3,5,8,13....

If we observe this sequence closely, Any term of this sequence is addition of previous two terms.

Suppose the term 3, the previous two terms are 2 + 1 = 3.

Similarly, for term 5, the previous two terms are 3 + 2 = 5.

So, next term of these sequence is 8 + 13 = 21

Next term of these sequence is 13 + 21 = 34

Next term of these sequence is 21 + 34 = 55

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

So, this is neither sequence.

Answer 3.

11, 9, 7, 5

See any term of this sequence is less than 2 from previous term.

So this is arithmetic sequence with common difference -2.

Like 11-2 = 9, similarly, 9 - 2 = 7, 7 - 2 = 5

So, next term is 5 - 2 = 3

3 - 2 = 1

1 - 2 = -1

-1 -2 = -3

-3 - 2 = -5

-5 - 2 = -7

11, 9, 7, 5, 3, 1, -1, -3, -5, -7