In an arithmetic progression, if the 2nd term is 8 and the 4th term is 14, what

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Question: In an arithmetic progression, if the 2nd term is 8 and the 4th term is 14, what is the 1st term?

Options:

Correct Answer: 6

Solution:

Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 3d = 14, solving gives a = 6.

In an arithmetic progression, if the 2nd term is 8 and the 4th term is 14, what is the 1st term?

In an arithmetic progression, if the 2nd term is 8 and the 4th term is 14, what is the 1st term?

Step 1: Understand that in an arithmetic progression (AP), each term is found by adding a common difference (d) to the previous term.
Step 2: Let the first term be 'a'. The second term can be expressed as 'a + d'.
Step 3: According to the question, the second term is 8. So, we can write the equation: a + d = 8.
Step 4: The fourth term can be expressed as 'a + 3d'.
Step 5: According to the question, the fourth term is 14. So, we can write the equation: a + 3d = 14.
Step 6: Now, we have two equations: a + d = 8 and a + 3d = 14.
Step 7: From the first equation (a + d = 8), we can express d as: d = 8 - a.
Step 8: Substitute d in the second equation (a + 3d = 14) with (8 - a): a + 3(8 - a) = 14.
Step 9: Simplify the equation: a + 24 - 3a = 14.
Step 10: Combine like terms: -2a + 24 = 14.
Step 11: Subtract 24 from both sides: -2a = 14 - 24, which simplifies to -2a = -10.
Step 12: Divide both sides by -2 to find a: a = 5.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Solving Linear Equations – The question tests the ability to set up and solve linear equations based on given terms of the arithmetic progression.