The sequence 5, 7, ______, 11 ...... n is an arithmetic progressionQuestion 9Answera.6b.9c.3d.10

1. Break Down the Problem

We need to find the missing term in the arithmetic progression (AP) sequence that starts with 5, 7, and continues with a term followed by 11. The known terms are 5, 7, and 11.

2. Relevant Concepts

In an arithmetic progression, the difference between consecutive terms is constant. This difference is referred to as the common difference (d).

The first term ($a$) is 5, the second term is 7, and we can denote the third term as $x$ and the fourth term as 11.

The formulas are:

• $d = a_2 - a_1$
• $a_3 = a_2 + d$
• $a_4 = a_3 + d$

3. Analysis and Detail

1. Calculate the common difference (d): $d = a_2 - a_1 = 7 - 5 = 2$

2. Use the common difference to find the missing term (third term, $x$): $a_3 = a_2 + d = 7 + 2 = 9$

3. Verify that the sequence is consistent by finding the fourth term: $a_4 = a_3 + d = 9 + 2 = 11$

4. Verify and Summarize

The calculations show that the missing term is $9$. The sequence is consistent with the definition of an arithmetic progression.

Final Answer

The missing term is 9 (option b).