Question:
In an A.P., if \(a = 8\) and \(a_{10} = -19\), then value of \(d\) is:
In an A.P., if \(a = 8\) and \(a_{10} = -19\), then value of \(d\) is:
Updated On: Jan 13, 2026
- \(3\)
- \(-\frac{11}{9}\)
- \(-\frac{27}{10}\)
- \(-3\)
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The Correct Option is D
Solution and Explanation
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:
\(d)\ -3\)
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