Q 15. Which is NOT an arithmetic sequence? $$ a_{n}=\{2,4,8,16,32, \ldots\} $$ $$ a_{n}=\{4,7,10,13,16, \ldots\} $$ $$ a_{n}=\{1,2,3,4,5, \ldots\} $$ $$ a_{n}=\{15,9,3,-3,-9, \ldots\} $$

Question

UpStudy AI · Accepted Answer

To determine which sequence is NOT an arithmetic sequence, we need to understand the definition of an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Let's analyze each sequence step by step:

1. **Sequence 1: $$ a_{n}=\{2,4,8,16,32, \ldots\} $$**
   - Differences: 
     - $$ 4 - 2 = 2 $$
     - $$ 8 - 4 = 4 $$
     - $$ 16 - 8 = 8 $$
     - $$ 32 - 16 = 16 $$
   - The differences are $$ 2, 4, 8, 16 $$, which are not constant. 
   - **Conclusion**: This is NOT an arithmetic sequence.

2. **Sequence 2: $$ a_{n}=\{4,7,10,13,16, \ldots\} $$**
   - Differences:
     - $$ 7 - 4 = 3 $$
     - $$ 10 - 7 = 3 $$
     - $$ 13 - 10 = 3 $$
     - $$ 16 - 13 = 3 $$
   - The differences are all $$ 3 $$, which is constant.
   - **Conclusion**: This is an arithmetic sequence.

3. **Sequence 3: $$ a_{n}=\{1,2,3,4,5, \ldots\} $$**
   - Differences:
     - $$ 2 - 1 = 1 $$
     - $$ 3 - 2 = 1 $$
     - $$ 4 - 3 = 1 $$
     - $$ 5 - 4 = 1 $$
   - The differences are all $$ 1 $$, which is constant.
   - **Conclusion**: This is an arithmetic sequence.

4. **Sequence 4: $$ a_{n}=\{15,9,3,-3,-9, \ldots\} $$**
   - Differences:
     - $$ 9 - 15 = -6 $$
     - $$ 3 - 9 = -6 $$
     - $$ -3 - 3 = -6 $$
     - $$ -9 - (-3) = -6 $$
   - The differences are all $$ -6 $$, which is constant.
   - **Conclusion**: This is an arithmetic sequence.

### Final Conclusion:
The sequence that is NOT an arithmetic sequence is:
$$
a_{n}=\{2,4,8,16,32, \ldots\}
$$
The sequence $$ \{2,4,8,16,32,\ldots\} $$ is NOT an arithmetic sequence.

Q 15. Which is NOT an arithmetic sequence?

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Pre Algebra Questions