Question

In an A.P., if \(a = 8\) and \(a_{10} = -19\), then value of \(d\) is:

• A. \(3\)
• B. \(-\frac{11}{9}\)
• C. \(-\frac{27}{10}\)
• D. \(-3\)

Answer 1

The Correct Option is D

In an arithmetic progression (A.P.), the \(n\)-th term is given by the formula:

\[ a_n = a + (n - 1)d \]

Where:

• \(a_n\) is the \(n\)-th term,
• \(a\) is the first term,
• \(d\) is the common difference.

We are given:

• \(a = 8\) (the first term),
• \(a_{10} = -19\) (the 10th term),
• We need to find \(d\) (the common difference).

 

Substitute the known values into the formula for the 10th term:

\[ a_{10} = a + (10 - 1)d \implies -19 = 8 + 9d \]

Now, solve for \(d\):

\[ -19 - 8 = 9d \implies -27 = 9d \implies d = -3 \]

Thus, the correct answer is:

\(d)\ -3\)