odd-number-2n-1-The-sum-of-twelve-consecutive-natural-numbers-is-288-Find-the-largest-natural-number-

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

o d d n u m b e r (2 n + 1)

The sum of twelve consecutive natural numbers is 288. Find the largest natural number

Answered by JDamian last updated on 16/Feb/23

Does it really exist ?

288 = \frac{12}{2} (n + n - 11) \Rightarrow

48 = 2 n - 11

n = \frac{59}{2} \notin N

19 + 20 + \cdot \cdot \cdot + 29 + 30 = 294

18 + 19 + \cdot \cdot \cdot + 28 + 29 = 282

Commented by mathlove last updated on 16/Feb/23

n = 12 f i n d a_{n}

Commented by JDamian last updated on 16/Feb/23

there is no such natural number a_n

Commented by MathsFan last updated on 17/Feb/23

thank you sir

Commented by mathlove last updated on 17/Feb/23

13 + 15 + 17 + 19 + 21 + 23 +

25 + 27 + 29 + 31 + 33 + 35 = 288

Commented by mr W last updated on 17/Feb/23

t h e n y o u r q u e s t i o n i s w r o n g!

Commented by JDamian 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) + \dots + (n + 11) = 288

12 n + 1 + 2 + \dots + 11 = 288

12 n + \frac{11 (11 + 1)}{2} = 288

12 n = 288 - 66

n = \frac{222}{12} = \frac{37}{2} \notin N

Commented by MathsFan last updated on 17/Feb/23

thanks a lot sir