Problem Statement:
Three blocks connected together lie on a horizontal frictionless table and are pulled to the right with a force f. We need to find the tension in the first and second block (t1 and t2, respectively).

Given:
- Three blocks connected together
- Blocks lie on a horizontal frictionless table
- Blocks are pulled to the right with a force f

Assumptions:
- The mass of each block is known
- The force f is known

Analysis:
To find the tension in the first and second block, we need to consider the forces acting on each block and analyze the equilibrium conditions.

Free Body Diagram:
A free body diagram for each block can be drawn to better understand the forces acting on them.

Block 1:
- Tension force T1 acts to the right
- Force of friction f1 acts to the left
- Weight W1 acts downwards

Block 2:
- Tension force T2 acts to the right
- Force of friction f2 acts to the left
- Weight W2 acts downwards

Block 3:
- Force of friction f3 acts to the left
- Weight W3 acts downwards

Equilibrium Conditions:
For each block to be in equilibrium, the net force acting on them in both horizontal and vertical directions should be zero.

Vertical Equilibrium:
Since the blocks are on a horizontal table, the weight acts in the downward direction, and the normal force exerted by the table acts in the upward direction. As the blocks are in equilibrium, the vertical forces are balanced, i.e., the weight is equal to the normal force.
Therefore, we can write the following equations:
- W1 = T1 + f1
- W2 = T2 + f2
- W3 = f3

Horizontal Equilibrium:
Considering the horizontal forces, the tension forces T1 and T2 contribute to the net force acting on the blocks, while the friction forces f1, f2, and f3 oppose the motion. As the blocks are in equilibrium, the horizontal forces are balanced, i.e., the net force is equal to zero.
Therefore, we can write the following equations:
- T1 + T2 - f1 - f2 - f3 = 0

Solution:
To find the tensions T1 and T2, we need to solve the above equations simultaneously. The values of masses and the force f would be provided in the problem, and by substituting those values into the equations, we can solve for T1 and T2 using algebraic methods.

Conclusion:
By considering the forces acting on each block and analyzing the equilibrium conditions, we can determine the tensions T1 and T2 in the given system of blocks connected together. The solution involves setting up equations based on the equilibrium conditions and solving them to find the unknown tensions.