Answer:
-10, 40, -240, 1,920 and -19, 200
Step-by-step explanation:
Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.
when n= 1;
aₙ₊₁ = -2naₙ
a₁₊₁ = -2(1)a₁
a₂ = -2(1)(5)
a₂ = -10
when n = 2;
a₂₊₁ = -2(2)a₂
a₃ = -2(2)(-10)
a₃ = 40
when n = 3;
a₃₊₁ = -2(3)a₃
a₄ = -2(3)(40)
a₄ = -240
when n= 4;
a₄₊₁ = -2(4)a₄
a₅ = -2(4)(-240)
a₅ = 1,920
when n = 5;
a₅₊₁ = -2(5)a₅
a₆ = -2(5)(1920)
a₆ = -19,200
Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200
Distance from Supermarket to Bank = 3 miles.
Distance from the Bank to the library = 4 miles.
Distance from the library back to supermarket =
![\sqrt{3^2 + 4^2} = 5](https://tex.z-dn.net/?f=%20%5Csqrt%7B3%5E2%20%2B%204%5E2%7D%20%20%3D%205)
Total Distance = 3 + 4 + 5 = 12 miles.
Answer: 12 miles
Answer: There are 126 red key chains.
Step-by-step explanation:
1. You know that 10% are yellow, then:
350*0.1=35 (35 key chains are yellow).
2. And you know that of the remaining key chains 3/5 there are green.
The remaining is:
350-35=315
Then:
325*3/5=189 (189 key chains are green).
3. Then, the number of key chains that are red is:
350-35-189=126 (126 key chains are red).