The sixth term of an A.P is half of its twelfth term. The first term of the A.P is equal to
The correct answer is D. the common difference
Let's denote the first term of the arithmetic progression (A.P.) as \(a\), and the common difference as \(d\).
The formula for the \(n\)th term of an arithmetic progression is given by:
\(a_n = a + (n-1)d\)
Given that the sixth term of the A.P. is half of its twelfth term, we can write this as:
\(a + 5d = \frac{1}{2} \cdot (a + 11d)\)
Simplify the equation:
\(2(a + 5d) = a + 11d\)
\(2a + 10d = a + 11d\)
Subtracting \(a\) and \(10d\) from both sides:
\(a = d\)
So, the first term of the A.P. is equal to the common difference.
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