The first 101 numbers of the Fibonacci sequence, because zero is the critical base:
0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368
75025
121393
196418
317811
514229
832040
1346269
2178309
3524578
5702887
9227465
14930352
24157817
39088169
63245986
102334155
165580141
267914296
433494437
701408733
1134903170
1836311903
2971215073
4807526976
7778742049
12586269025
20365011074
32951280099
53316291173
86267571272
139583862445
225851433717
365435296162
591286729879
956722026041
1548008755920
2504730781961
4052739537881
6557470319842
10610209857723
17167680177565
27777890035288
44945570212853
72723460248141
117669030460994
190392490709135
308061521170129
498454011879264
806515533049393
1304969544928657
2111485077978050
3416454622906707
5527939700884757
8944394323791464
14472334024676221
23416728348467685
37889062373143906
61305790721611591
99194853094755497
160500643816367088
259695496911122585
420196140727489673
679891637638612258
1100087778366101931
1779979416004714189
2880067194370816120
4660046610375530309
7540113804746346429
12200160415121876738
19740274219868223167
31940434634990099905
51680708854858323072
83621143489848422977
135301852344706746049
218922995834555169026
354224848179261915075
Answer 144 which is F(12) Reason 55 and 89 are the 10th and 11th Fibonacci numbers, If we add these we have 144 which is the 12 Fibonacci number and is a perfect square. I am using F(0) as the 0 Fibonacci number and F(1) as the first.
Multiply by 5 4*5 = 20 20*5 = 100 100*5 = 500 500*5 = 2500
The first thing to notice is that all the numbers in the sequence are square numbers. 25=5x5 36=6x6 49=7x7 64=8x8 81=9x9 So the next three numbers to be squared are 10, 11 and 12. 10x10=100 11x11=121 12x12=144 Thus, the next three numbers in the sequence are 100, 121, 144 The equation for the sequence is (n+4)2
They are square numbers
S = 955 This is an arithmetic sequence, and the sum of an arithmetic sequence can be calculated as: S = n/2 x (U1 + Un) U1 is the first term (in this case 91) and Un is the last term (in this case 100). n presents the total number of terms in the sequence There are 10 numbers in this sequence (91, 92, 93, 94, 95, 96, 97, 98, 99, 100) So, the sum is : S = 10/2 x (91+100) = 955
Answer 144 which is F(12) Reason 55 and 89 are the 10th and 11th Fibonacci numbers, If we add these we have 144 which is the 12 Fibonacci number and is a perfect square. I am using F(0) as the 0 Fibonacci number and F(1) as the first.
The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.
The Fibonacci numbers below 100 are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987
The first thing to notice is that all the numbers in the sequence are square numbers. 25=5x5 36=6x6 49=7x7 64=8x8 81=9x9 So the next three numbers to be squared are 10, 11 and 12. 10x10=100 11x11=121 12x12=144 Thus, the next three numbers in the sequence are 100, 121, 144 The equation for the sequence is (n+4)2
They are square numbers
1, 2, 3, 5, 8, 13, 21, 34, 55, and 89 are.
25 36 49 64 81 100 121 144
It is a sequence of numbers where the difference between successive numbers is decreasing by one.
The first 100 odd whole numbers are: 13579111315171921232527293133353739414345474951535557596163656769717375777981838587899193959799101103105107109111113115117119121123125127129131133135137139141143145147149151153155157159161163165167169171173175177179181183185187189191193195197199.
The first 100 even numbers are: 2 468101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200.
The first 100 whole, even numbers are: 2468101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200.
S = 955 This is an arithmetic sequence, and the sum of an arithmetic sequence can be calculated as: S = n/2 x (U1 + Un) U1 is the first term (in this case 91) and Un is the last term (in this case 100). n presents the total number of terms in the sequence There are 10 numbers in this sequence (91, 92, 93, 94, 95, 96, 97, 98, 99, 100) So, the sum is : S = 10/2 x (91+100) = 955