Equation - integers

Solve the equation with the unknown x from the field of natural numbers 1+6+11+16+. ... +x=970

Final Answer:

x =  96

Step-by-step explanation:

s=970 d=61=5 a1=1 a2=a1+d=1+5=6 a3=a2+d=6+5=11 a4=a3+d=11+5=16  an = a1+(n1) d = 1+(n1) 5 = 1 + 5n5 = 5n4  s = 2a1+an n  2 s=(a1+5n4) n  2 970=(1+5n4) n 5n2+3n+1940=0 5n23n1940=0  a=5;b=3;c=1940 D=b24ac=3245(1940)=38809 D>0  n1,2=2ab±D=103±38809 n1,2=103±197 n1,2=0.3±19.7 n1=20 n2=19.4  n=n1=20  x=a1+(n1) d=1+(201) 5=96   Verifying Solution:   s96=2a1+x n=21+96 20=970

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