372.

Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24^th term.

Given: S₂₀ = -240  and a = 7

Consider,  S₂₀ = -240

$$\begin{gathered} {\mathrm{S}}_{\mathrm{n}} = \frac{\mathrm{n}}{2}\left[2\mathrm{a} + (\mathrm{n}-1) \mathrm{d}\right] \\ \Rightarrow -240 = \frac{20}{2}\left[2 \mathrm{x} 7 + (20-1) \mathrm{d}\right] \\ \Rightarrow -240 = 10 (14 + 19\mathrm{d}) \\ \Rightarrow -24 = 14 + 19\mathrm{d} \\ \Rightarrow -24 - 14 = 19\mathrm{d} \\ \Rightarrow 19\mathrm{d} = -38 \\ \Rightarrow \mathrm{d}= -2 \end{gathered}$$

Now, a₂₄ = a + 23d

              = 7 + 23 x (-2)

              = -39

Hence, a₂₄ = -39