Find the 25th term of the AP 5, \(4\frac{1}{2},4,3\frac{1}{2},3\),...

1.	Find the 25th term of the AP 5, \(4\frac{1}{2},4,3\frac{1}{2},3\),........
Answer» The given AP is 5, \(4\frac{1}{2},4,3\frac{1}{2},3\),........ First term = 5 Common difference = \(4\frac{1}{2}-5\Rightarrow \frac{9}{2}-5\) \(\Rightarrow \frac{9\,-\,10}{2}=-\frac{1}{2}\) ∴ a = 5 and d = \(-\frac{1}{2}\) Now, T₂₅ = a + (25 - 1) d = a + 24d \(=5+24\times(-\frac{1}{2})=5-12=-7\) ∴ 25^th term = -7

Find the 25th term of the AP 5, \(4\frac{1}{2},4,3\frac{1}{2},3\),........

Answer»

The given AP is 5, \(4\frac{1}{2},4,3\frac{1}{2},3\),........

First term = 5

Common difference = \(4\frac{1}{2}-5\Rightarrow \frac{9}{2}-5\) \(\Rightarrow \frac{9\,-\,10}{2}=-\frac{1}{2}\)

∴ a = 5 and d = \(-\frac{1}{2}\)

Now, T₂₅ = a + (25 - 1) d = a + 24d

\(=5+24\times(-\frac{1}{2})=5-12=-7\)

∴ 25^th term = -7