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Question Number 11399 by tawa last updated on 23/Mar/17

The sum of the first and last term of an A.P is 51. And the sum of the   progression is 255. Find the last term of the A.P.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{last}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}\:\mathrm{is}\:\mathrm{51}.\:\mathrm{And}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{progression}\:\mathrm{is}\:\mathrm{255}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$

Answered by ajfour last updated on 23/Mar/17

last term = (1/2)(51+9d)  where d is whatever common  diffeeence you choose..  number of terms n=10  The first term a= (1/2)(51−9d)

$$\mathrm{last}\:\mathrm{term}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{51}+\mathrm{9d}\right) \\ $$$$\mathrm{where}\:\mathrm{d}\:\mathrm{is}\:\mathrm{whatever}\:\mathrm{common} \\ $$$$\mathrm{diffeeence}\:\mathrm{you}\:\mathrm{choose}.. \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{n}=\mathrm{10} \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{a}=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{51}−\mathrm{9d}\right) \\ $$

Commented by tawa last updated on 24/Mar/17

God bless you sir.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$$$ \\ $$

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