Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 11930 by 786786AM last updated on 05/Apr/17

$$\mathrm{Let}\mathrm{a}\mathrm{and}\mathrm{b}\mathrm{be}\mathrm{two}\mathrm{numbers},\mathrm{x}\mathrm{be}\mathrm{the}\mathrm{single}\mathrm{arithmetic}\mathrm{mean}\mathrm{of}\mathrm{a}\mathrm{and}\mathrm{b}.$$$$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{n}\mathrm{arithmetic}\mathrm{means}\mathrm{between}\mathrm{a}\mathrm{and}\mathrm{b}\mathrm{is}\mathrm{nx}.$$

Answered by ajfour last updated on 05/Apr/17

$$A_r=a+\frac{(b-a)}{(n+1)}r$$$$\underset{r=1}{\sum ^n}{A}_r=na+\frac{(b-a)}{(n+1)}.\frac{n(n+1)}{2}$$$$=na+\frac{n(b-a)}{2}$$$$=\frac{n(a+b)}{2}=nx.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com