crowntinyy3557 crowntinyy3557
  • 13-04-2019
  • Mathematics
contestada

BRAINLIEST pleae help!!!

The sum of 27 consecutive odd integers is 3^9=19683. Compute the least of these consecutive odd integers.

The answer is 703

Respuesta :

DeanR
DeanR DeanR
  • 13-04-2019

I had a whole answer and my tab crashed.  Hate that.

We'll use the known sum of the first n natural numbers,

[tex]\displaystyle \sum_{k=1}^{n} k = \dfrac{n(n+1)}{2}[/tex]

Let a be the first number, the one we seek.

[tex]\displaystyle 3^9= \sum_{k=0}^{26} (a+2k) = 27a+ 2 \sum_{k=1}^{26}k[/tex]

[tex]\displaystyle 3^9=27a+2(26)(26+1)/2 [/tex]

[tex]3^9=27(a+26) [/tex]

[tex]3^6= a+ 26[/tex]

[tex]a = 3^6 - 26[/tex]

[tex]a = 703 \quad\checkmark[/tex]

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