Question

​if the first term of an ap is -4 and the common difference is 2 then find the sum of its first 10 terms

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a}\mathrm{be}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and}\mathrm{d}\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{difference}. \\ \mathrm{Now},\mathrm{a}=-4;\mathrm{d}=2 \\ \mathrm{Now},\mathrm{sum}\mathrm{of}\mathrm{first}\mathrm{n}\mathrm{terms}\mathrm{of}\mathrm{AP}\mathrm{is}\mathrm{given}\mathrm{by} \\ {\mathrm{S}}_{\mathrm{n}}=\frac{\mathrm{n}}{2}\left[2\mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d}\right] \\ \Rightarrow {\mathrm{S}}_{10}=\frac{10}{2}\left[2\left(-4\right)+\left(10-1\right)\left(2\right)\right] \\ =5\left(-8+18\right) \\ =5\times 10 \\ =50 \end{gathered}$$