Question

Indicate whether the sequence is arithmetic, geometric, or neither, Give the next two terms in the sequence. 9) 1, 8, 15, 22, 29,... 9) 10) 5, 15, 45, 135, 405,... 10) 11) 13, 14,21, 28, 35,.. 11) 12) 12) 15, 75, 375, 1875, 9375,...

Answer 1

1) arithmetic. 36, 43.

2) geometric. 1215, 3645.

3) neither.

4) geometric. 6875, 234375.

Explanation:

First, let's remember the definition of both arithmetic and geometric sequence.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed value.

An arithmetic sequence is a sequence of numbers where each term is found by adding a fixed value to the previous term.

Now, let's examine the sequences given:

1, 8, 15, 22, 29,.. this is an arithmetic sequence (adding 7 to each term), the next two terms would be 36, 43.

5, 15, 45, 135, 405... this is a geometric sequence (multiplying by 3). The next two terms are: 1215, 3645

13, 14,21, 28, 35,.. this is neither a geometric or an arithmetic sequence (if it hadn't 13 as a first term then it would be an arithmetic sequence and the next two numbers would be 42, 49)

15, 75, 375, 1875, 9375,.. this is a geometric sequence (multiplying by 5). The next two terms are 46875, 234375.