Question

If the numbers n – 3, 4n – 2 and 5n + 1 are in arithmetic progression, then the value of n is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is A

To find the value of n such that the numbers n – 3, 4n – 2, and 5n + 1 are in arithmetic progression, we need to use the property of an arithmetic progression, which states that twice the middle term is equal to the sum of the first and third terms. 

This can be expressed as:

2(4n - 2) = (n - 3) + (5n + 1)

Expanding both sides, we get:

8n - 4 = n - 3 + 5n + 1

Simplifying further,

8n - 4 = 6n - 2

To solve for n, subtract 6n from both sides:

8n - 6n - 4 = -2

2n - 4 = -2

Adding 4 to both sides gives:

2n = 2

Dividing both sides by 2 to solve for n, we get:

n = 1

Thus, the value of n is 1.

Answer 2

Given that the numbers \( n - 3 \), \( 4n - 2 \), and \( 5n + 1 \) are in arithmetic progression (A.P.), their common difference must be equal.

In an A.P., the difference between consecutive terms is the same:

\( (4n - 2) - (n - 3) = (5n + 1) - (4n - 2) \) 

Simplify both sides:

\( 4n - 2 - n + 3 = 5n + 1 - 4n + 2 \)

\( 3n + 1 = n + 3 \)

Solving for \( n \):

\( 3n - n = 3 - 1 \)

\( 2n = 2 \)

\( n = 1 \)

Thus, the value of \( n \) is: \( 1 \).