Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 62664 by Cheyboy last updated on 24/Jun/19

$$Findthenthterm$$$$100,92,76,44,......$$

Answered by MJS last updated on 24/Jun/19

$$a_n=108-4\times 2^n$$$$a_n=-\frac{4}{3}{n}^3+4n^2-\frac{32}{3}n+108$$$$...$$

Commented by ajfour last updated on 24/Jun/19

wonderful sir! how to expect and judge the first one?

Commented by mr W last updated on 24/Jun/19

$$100=104-2^2$$$$92=100-2^3=104-(2^2+2^3)$$$$76=92-2^4=104-(2^2+2^3+2^4)$$$$...$$$$a_n=104-(2^2+2^3+2^4+...+2^{n+1})$$$$=104-\frac{2^2(2^n-1)}{2-1}=108-2^{n+2}$$

Commented by MJS last updated on 24/Jun/19

$$\mathrm{we}\mathrm{can}\mathrm{solve}$$$$\underset{i=1}{\sum ^4}{c}_i=100$$$$\underset{i=1}{\sum ^4}{c}_i^2=92$$$$\underset{i=1}{\sum ^4}{c}_i^3=76$$$$\underset{i=1}{\sum ^4}{c}_i^4=44$$$$\mathrm{using}{c}_{1,2}=\alpha \pm \sqrt{\beta };c_{3,4}=\gamma \pm \sqrt{\delta }$$$$\Rightarrow a_n=\underset{i=1}{\sum ^4}{c}_i^n$$$$\mathrm{but}\mathrm{the}\mathrm{solution}{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{look}\mathrm{very}\mathrm{nice}$$

Commented by Cheyboy last updated on 25/Jun/19

$$Thankyouverymuch$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com