Question

If the 10^th and 12^th terms of an A.P. are respectively 15 and 21, then the common difference of the A.P. is

• A. -6
• B. 4
• C. 6
• D. -3
• E. 3

Answer 1

Answer: (E)

We are given that the 10^th and 12^th terms of an arithmetic progression (A.P.) are 15 and 21, respectively. We are asked to find the common difference of the A.P. 

The formula for the \(n-\) term of an A.P. is:

\(t_n = a_1 + (n-1) d\)

where \(t_n\) is the \(n-\) term, \(a_1\) is the first term, and \(d\) is the common difference.

We are given:

• \(t_{10} = 15\)
• \(t_{12} = 21\)

Using the formula for the \(n-\) term, we can write two equations:

\(t_{10} = a_1 + (10-1) d = a_1 + 9d = 15\)

\(t_{12} = a_1 + (12-1) d = a_1 + 11d = 21\)

Now, we have the system of equations:

• \(a_1 + 9d = 15\)
• \(a_1 + 11d = 21\)

Subtract the first equation from the second to eliminate \(a_1\):

\((a_1 + 11d) - (a_1 + 9d) = 21 - 15\)

\(2d = 6\)

\(d = 3\)

The common difference of the A.P. is 3.