1+2=3
2+3=5
3+4=7
4+7= 1 1
7+6= 13
6+ 1 1= 17
The sum of the two terms is a prime number, arranged in order of size.
② 0,0,6,24,60, 120(2 10 or 336)
Method 1:
0-0=0
6-0=6
24-6= 18
60-24=36
120-60=60
From 0, 6, 18, 36, 60,
We know: 6× 0, 6× 1, 6× (1+2), 6× (1+2+3), 6× (1+2+4),
The difference of the latter term should be 6×( 1+2+3+4+5)=90.
So x- 120=90.
Find x=2 10.
Method 2:
0=0? -0
0= 1? - 1
6=2? -2
24=3? -3
60=4? -4
120=5? -5
2 10=6? -6
Know the general formula: n? Tong -EN
Method 3:
(- 1)×0× 1=0
0× 1×2=0
1×2×3=6
2×3×4=24
3×4×5=60
4×5×6= 120
5×6×7=2 10
6×7×8=336
So the answer to this question is: 0, 0, 6, 24, 60, 120 (2 10 or 336).
③-2,- 14,-24,4, 130,438,( 1036)
1^3×(-3)+ 1=-2
2^3×(-2)+2=- 14
3^3×(- 1)+3=-24
4^3×0+4=4
5^3× 1+5= 130
6^3×2+6=438
7^3×3+7= 1036
④5,67,37,5 15, 10 1( 173 1)
2^2+ 1=5
4^3+3=67
6^2+ 1=37
8^3+3=5 15
10^2+ 1= 10 1
12^3+3= 173 1
⑤ 14,20,54,76,( 126)
3^2+5= 14
5^2-5=20
7^2+5=54
9^2-5=76
1 1^2+5= 126
⑥2,3,2,4,(5),(4),2,7
(2-3)^2+ 1=2
(3-2)^2+3=4
(2-4)^2+ 1=5
(4-5)^2+3=4
(5-4)^2+ 1=2
(4-2)^2+3=7
From the third term, we can see that the latter term is the square of the difference between the first two terms (odd term+1, even term +3), which shows its law.
Honey, do you understand?