Question

Find the 25^th term of the AP \[- 5, \frac{- 5}{2}, 0, \frac{5}{2}, . . .\]

 

Answer 1

\[Here, a = - 5\]
\[d = \frac{- 5}{2} - \left( - 5 \right) = \frac{- 5}{2} + 5 = \frac{5}{2}\]
\[Now, a_n = a + \left( n - 1 \right)d\]
\[ \therefore a_{25} = - 5 + \left( 25 - 1 \right) \times \frac{5}{2}\]
\[ \Rightarrow a_{25} = - 5 + 24 \times \frac{5}{2}\]
\[ \Rightarrow a_{25} = - 5 + 60\]
\[ \Rightarrow a_{25} = 55\]

Thus, the 25th term of the given AP is 55.