Question

14, 17, 20, 23 .......

1. The common difference in the sequence above is
2. The 4th term in the sequence is
3. A formula that I create to describe this sequence is \large f\left(x\right) =
4. The value of the 100th term is

Answer 1

1. The common difference in the sequence is 3. (Each term is 3 greater than the previous term.)

2. The 4th term in the sequence is 23.

3. A formula to describe this arithmetic sequence is:

\(f(x) = 14 + 3(x-1)\)

This formula represents an arithmetic sequence with an initial term of 14 and a common difference of 3.

4. To find the 100th term in the sequence, you can use the formula for an arithmetic sequence:

\(a_n = a_1 + (n-1)d\)

Where:

- \(a_n\) is the nth term,

- \(a_1\) is the first term,

- n is the term number,

- d is the common difference.

In this case, \(a_1 = 14\), the common difference \(d = 3\), and we want to find the 100th term (\(n = 100\)):

\(a_{100} = 14 + (100-1) \cdot 3\)

\(a_{100} = 14 + 99 \cdot 3\)

\(a_{100} = 14 + 297\)

\(a_{100} = 311\)

So, the value of the 100th term in the sequence is 311.

Explanation: