Arithmetic Progression

To solve the problem, we need to find the sum of the first 15 terms of the arithmetic progression (A.P.) 3, 6, 9, ...

1. Identifying the First Term and Common Difference:
First term
Common difference

2. Using the Formula for Sum of First Terms:
The sum of the first terms of an A.P. is given by:

3. Substituting the Values:
Let , ,

Final Answer:
The sum of 15 terms of the A.P. is 360 (Option B).

To solve the problem, we need to find the term of an arithmetic progression (A.P.) given:

• First term
• term

1. General Formula for the Term:
The general term of an A.P. is given by:


where is the first term and is the common difference.

2. Use the Given Term:
We know :


Substitute :

3. Finding the Term:
Use the formula again:

Final Answer:
The term is .

To solve the problem, we need to find the sum of the first 10 terms of the Arithmetic Progression (A.P.): 2, 7, 12, ...

1. Identifying the First Term and Common Difference:
The first term
The common difference

2. Using the Formula for Sum of First n Terms of A.P.:
The formula is:

Substituting the known values ( , , ):

Final Answer:
The sum of the first 10 terms is

Step 1: Identify the first term (a) and common difference (d) of the A.P.
First term,
Common difference,

Step 2: Use the formula for the term of an A.P.:


Step 3: Plug in :

The correct option is (A):