Question

1+3+5+…+x=256, afla x-ul.

Answer 1

a1 = 1 ; a2 = 3 => r = a2-a1 = 2
Suma = 1+3+5+.....+x = 256
S = (1+x)(x+1)/2*2
1+x = primul+ultimul termen
(x+1)/2 = numarul de termeni
S = (x+1)² / 4 = 256 => x²+2x +1 = 256*4 = 1024 => x²+2x-1023 =0
x=[-2 +√(4+4092)]/2 =(-2+64)/2 => x = 62/2 => x = 31


S=1+3+5+....+31 = 256 , verificat , e corect.

Answer 2

O sumă de Nr impare consecutive este egală cu Nr de termeni la pătrat
=> n^2=256 =>n=16. => (X-1)/2+1=16 =>( x-1)/2=15 => x-1=30 => x=31