If the 9th term of an A.P is five times the 5th term, find the relationship between a and d.
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Correct Answer: Option C
Explanation:
\(T_{n} = a + (n - 1) d\) (nth term of an AP).
\(T_{9} = 5T_{5}\)
\(a + 8d = 5(a + 4d) \implies a + 8d = 5a + 20d\)
\(5a - a + 20d - 8d = 0 \implies 4a + 12d = 0\)
\(a + 3d = 0\)
\(T_{n} = a + (n - 1) d\) (nth term of an AP).
\(T_{9} = 5T_{5}\)
\(a + 8d = 5(a + 4d) \implies a + 8d = 5a + 20d\)
\(5a - a + 20d - 8d = 0 \implies 4a + 12d = 0\)
\(a + 3d = 0\)