Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 204348 by BaliramKumar last updated on 14/Feb/24

$$3\times 7\times 11+7\times 11\times 15+11\times 15\times 19+..........+39\times 43\times 47=?$$

Answered by MM42 last updated on 14/Feb/24

$$\underset{1}{\sum ^{10}}(4n-1)(4n+3)(4n+7)$$$$=\underset{1}{\sum ^{10}}(64n^3+14n^2+44n-21)$$$$=64\times {\left(\frac{10\times 11}{2}\right)}^2+14\times \frac{10\times 11\times 21}{6}+44\times \frac{10\times 11}{2}-210$$$$$$

Commented by BaliramKumar last updated on 14/Feb/24

$$\mathrm{thanks}\mathrm{sir}$$$$\mathrm{typo}14\to 144$$$$\mathrm{also}\frac{39\times 43\times 47\times (47+\mathrm{d})}{\mathrm{d}\cdot \mathrm{t}}-\frac{(3-\mathrm{d})\times 3\times 7\times 11}{\mathrm{d}\cdot \mathrm{t}}$$$$\mathrm{d}=\mathrm{difference}=4$$$$\mathrm{t}=\mathrm{no}.\mathrm{of}\mathrm{terms}=3+1=4$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com