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Question Number 187390 by mathlove last updated on 18/Feb/23

$$oddnumber(2n+1)$$ The sum of twelve consecutive natural numbers is 288. Find the largest natural number\n

Answered by JDamian last updated on 16/Feb/23

$$\mathrm{Does}\mathrm{it}\mathrm{really}\mathrm{exist}?$$ $$$$ $$288=\frac{12}{2}(n+n-11)\Rightarrow$$ $$48=2n-11$$ $$n=\frac{59}{2}\notin \mathbb{N}$$ $$19+20+\cdot \cdot \cdot +29+30=294$$ $$18+19+\cdot \cdot \cdot +28+29=282$$

Commented bymathlove last updated on 16/Feb/23

$$n=12find{a}_n$$

Commented byJDamian last updated on 16/Feb/23

there is no such natural number a_n

Commented byMathsFan last updated on 17/Feb/23

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

Commented bymathlove last updated on 17/Feb/23

$$13+15+17+19+21+23+$$ $$25+27+29+31+33+35=288$$

Commented bymr W last updated on 17/Feb/23

$$thenyourquestioniswrong!$$

Commented byJDamian last updated on 19/Feb/23

Mathlove, do you even check your questions and solutions before posting them?

Answered by HeferH last updated on 16/Feb/23

$$n+(n+1)+(n+2)+...+(n+11)=288$$ $$12n+1+2+...+11=288$$ $$12n+\frac{11(11+1)}{2}=288$$ $$12n=288-66$$ $$n=\frac{222}{12}=\frac{37}{2}\notin \mathbb{N}$$

Commented byMathsFan last updated on 17/Feb/23

$$\mathrm{thanks}\mathrm{a}\mathrm{lot}\mathrm{sir}$$

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