Question

find the sum of first 10 composite no

Answer 1

Dear student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{The}\mathrm{first}10\mathrm{composite}\mathrm{numbers}\mathrm{are},4,6,8,9,10,12,14,15,16,18 \\ \mathrm{so}\mathrm{we}\mathrm{have}; \\ 4+6+8+9+10+12+14+15+16+18 \\ =\left(4+6+8+10+12+14+16+18\right)+9+15 \\ =\frac{8}{2}\left[2\times 4+\left(8-1\right)\times 2\right]+9+15\{\mathrm{Here},\mathrm{first}\mathrm{term},\mathrm{a}=4;\mathrm{common}\mathrm{difference},\mathrm{d}=2\mathrm{and}\mathrm{number}\mathrm{of}\mathrm{terms},\mathrm{n}=8\mathrm{and}\mathrm{using}\mathrm{the}\mathrm{formula}{\mathrm{S}}_{\mathrm{n}}=\frac{\mathrm{n}}{2}\left[2\mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d}\right]\} \\ =4\times 22+9+15 \\ =112 \\ \mathrm{Therefore}\mathrm{sum}\mathrm{of}\mathrm{first}10\mathrm{composite}\mathrm{numbers}=112 \end{gathered}$$
Regards