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

Question

For some positive and distinct real numbers \(x ,y\), and \(z\) , if \(\frac{1}{\sqrt{ y}+ \sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+ \sqrt{z}}\) and \(\frac{1}{\sqrt{x} +\sqrt{y}}\) , then the relationship which will always hold true, is

Answer 1

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

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

Where:

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

Given information:

First term, \(a = 8\),
10th term, \(a_{10} = -19\).
Objective: Find the common difference, \(d\).

Applying the formula for the 10th term with the given values:

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

Solving for \(d\):

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

The common difference is:

\(d = -3\)

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

The Correct Option is D

Solution and Explanation

Top Questions on Arithmetic Progression

Questions Asked in CBSE Class X exam