Sequence Tenth Term Calculation

The problem asks for the 10th term of the sequence 2, 5, 8, 11, ....

Identifying Sequence Properties

This sequence is an Arithmetic Progression (AP) because the difference between consecutive terms is constant.

• First term ($a$): 2
• Common difference ($d$): $5 - 2 = 3$.

Arithmetic Progression Formula

The formula to find the $n$-th term ($a_n$) of an AP is:

Where:

• $a_n$ is the n-th term
• $a$ is the first term
• $n$ is the term number
• $d$ is the common difference

Calculating the Tenth Term

We need to find the 10th term, so $n=10$. Plugging the values into the formula:

$ a_{10} = 2 + (10-1) \times 3 $

$ a_{10} = 2 + (9) \times 3 $

$ a_{10} = 2 + 27 $

$ a_{10} = 29 $

Final Answer

The tenth term of the sequence is 29.