Question

Proszę o jak najszybsze rozwiązanie

Answer 1

1. (2n/5)8 > 10
2n/5 > 10/8
2n > 50/8
n > 50/16
n > 3 ⅛

Odp: Od 4 wyrazu ciągu.

2. an = n² + 3n - 10
a(n+1) = (n+1)² + 3(n+1) - 10 = n²+2n+1+3n+3-10 = n²+5n-6

a(n+1) - an = n²+3n-10 - n²-5n+6 = -2n-4 = (-)
malejący.

3. an = 5n+3
S = 6272

a₁ = 5+3 = 8

6272 = n(8+5n+3)/2
12544 = n(11+5n)
12544 = 11n + 5n²
5n² + 11n - 12544 = 0
Δ = 121 - 4*5*(-12544) = 251001

n₁ = (-11 - 501)/2*5 <---- odpada, bo n musi być dodatnie
n₂ = (-11+501)/10 = 49

4. (a₁+4r) - (a₁+r) = -6
a₁ + a₁+3r = 0

a₁+4r-a₁-r = -6
2a₁+3r = 0

3r = -6
2a₁ - 6 = 0

a₁ = 3
r = -2

an = 3 - 2(n-1)
an = 3 - 2n + 2
an = 5-2n

5. a² = 4*9
9² = ab

a² = 36
a = 6

81 = 6b
b = 81/6
b = 13½

6. a(n+1) = 3*5^(n+1-1) = 3*5^n
an = 3*5^(n-1)

n(n+1)/an = (3*5^n)/(3*5^(n-1)) = 5^n/ [(5^n)/5] = 5 * 5^n/ 5^n = 5

jest geometryczny