Question

1. create your own arithmetic sequence (list of numbers). remember arithmetic means it has the same common difference/change.

for problems 12 - 15, write the recursive form for the following sequences.
***** write what you see and change the d*****

1. 24, 20, 16, 12
2. 7, 13, 19, 25
3. d = 5 a6 = -2
4. d = -7 a9 = 22

find the next term of each sequence by using the recursive formula.

1. 100, 200, 300, 400,
2. -6, -12, -18, -24,
3. 55, 70, 85, 100,
4. 15, 11, 7, 3,
5. find a1 if a32 = 622 and d = 20.

Explanation:

11.

Step1: Choose a first - term and a common difference

Let \(a_1 = 3\) and \(d = 4\).

Step2: Generate the arithmetic sequence

The arithmetic sequence is \(3,7,11,15,19,\cdots\)

12.

Step1: Identify the first - term and common difference

\(a_1=24\), \(d = 20 - 24=-4\)

Step2: Write the recursive formula

The recursive formula for an arithmetic sequence is \(a_n=a_{n - 1}+d\). So \(a_1 = 24\), \(a_n=a_{n - 1}-4\) for \(n\geq2\)

13.

Step1: Identify the first - term and common difference

\(a_1 = 7\), \(d=13 - 7 = 6\)

Step2: Write the recursive formula

\(a_1 = 7\), \(a_n=a_{n - 1}+6\) for \(n\geq2\)

14.

Answer:

1. \(3,7,11,15,19,\cdots\)
2. \(a_1 = 24\), \(a_n=a_{n - 1}-4\) for \(n\geq2\)
3. \(a_1 = 7\), \(a_n=a_{n - 1}+6\) for \(n\geq2\)
4. \(a_1=-27\), \(a_n=a_{n - 1}+5\) for \(n\geq2\)
5. \(a_1 = 78\), \(a_n=a_{n - 1}-7\) for \(n\geq2\)
6. \(500\)
7. \(-30\)
8. \(115\)
9. \(-1\)
10. \(2\)