Find the common difference of the following ap 4,4,4

General
1

find the common difference of the following ap 4,4,4

2

Find the Common Difference of the Following AP: 4, 4, 4

Answer:

An Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms remains constant. This constant difference is known as the common difference, denoted by d.

The general formula for the common difference in an AP is:

d = a_{n+1} - a_n

Where:

  • (a_n) is the current term.
  • (a_{n+1}) is the next term.

For the given sequence 4, 4, 4, let us calculate the common difference step-by-step:

Step 1: Identify the Consecutive Terms

  • Let (a_1 = 4), (a_2 = 4), (a_3 = 4).

Step 2: Apply the Formula for Common Difference

We calculate (d) using (a_{n+1} - a_n):

d = a_2 - a_1 = 4 - 4 = 0

Similarly:

d = a_3 - a_2 = 4 - 4 = 0

Step 3: Conclusion

Since the difference between any two consecutive terms in the sequence is zero, the common difference (d) for this Arithmetic Progression (AP) is:

\boxed{0}

Properties of This AP

  • Constant Terms: Since all terms in the sequence are the same ((4, 4, 4)), the AP is a constant sequence.
  • Zero Common Difference: A constant sequence always has a common difference of 0.
  • Formula for (n)-th Term: The general term of this AP is given by:
    a_n = a_1 + (n-1) \cdot d
    Substituting ((a_1 = 4), (d = 0)):
    a_n = 4 + (n-1) \cdot 0 = 4
    This confirms that all terms in the sequence are equal to 4.

Applications

  • This type of sequence is useful in problems where the values remain unchanged, such as constant rates of change over time or repetitive measurements.

Let me know if you need further explanations! :blush:

@anonymous13