What is the common difference given that the 11th term of an arithmetic progression is 43 and that the first term is 3?

The common difference is 4.

Understanding Arithmetic Progressions (AP)

An arithmetic progression is a sequence of numbers where the difference between consecutive terms remains constant. This constant difference is called the common difference. The formula for the nth term of an arithmetic progression is:

a_n = a₁ + (n-1)d

where:

• a_n is the nth term
• a₁ is the first term
• n is the term number
• d is the common difference

Calculating the Common Difference

We are given that the 11th term (a₁₁) is 43 and the first term (a₁) is 3. We can use the formula to solve for the common difference (d):

1. Substitute the known values: 43 = 3 + (11-1)d
2. Simplify: 43 = 3 + 10d
3. Solve for d: 40 = 10d => d = 4

Therefore, the common difference is 4. This means each term in the sequence is 4 more than the previous term.

Example Sequence

The arithmetic progression would begin: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43...

Each term is obtained by adding 4 to the preceding term.