Question

1. Determina numarul natural n , stiind ca : 5^n+5^n+1+5^n+2=775
2. Calculeaza : 5^0+5^1+5^2+5^3+5^4
3. Determina numarul matural n stiind ca : 7^n+3=7^7

Answer 1

1)
5^n + 5^n+1 + 5^n+2 = 775
5^n ×(1+5^1 +5^2) = 775
5^n×(1+5+25) = 775
5^n×31 = 775
5^n = 775 : 31
5^n = 25
5^n = 5^2
n = 2

2)
5^0 + 5^1 + 5^2 + 5^3 + 5^4 =
= 1 + 5^1×(1+5+5^2+5^3) =
= 1 + 5 × (6+25+125) =
= 1 + 5 × 156 =
= 1 + 780 =
= 781

3)
7^n+3 = 7^7
n + 3 = 7
n = 7-3
n = 4