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International Journal of Computational Engineering Research||Vol, 03||Issue, 5||
N
N
2
t 20, n [9 n 8 n ]
n1 n1
N
n 1
N
N
2
9 n 8
n1 n1
N ( N
9
1)( 2 N 1) N ( N
8
1)
2 2
4
t 2 0 , n 9 p N 8t3,
N
6 5
t2 0 , n t1 2 , n 4 t7 , n t1 1, n 2 5 cp n 2 2 p n
2.
Proof
n
3 2
t2 0 , n t1 2 , n 4 t7 , n t1 1, n 1 4 n 1 1n
3 3 2
2 5 n 1 1 n n
6 5
t2 0 , n t1 2 , n 4 t7 , n t1 1, n 2 5 cp n 2 2 p n
3. t 2 0 , n 1 2 t1 1, n g n 1 5 n 2
Proof
2
t2 0 , n 1 9 n 1 0 n 1
2
9 n 7 n 2 n 1 1 5 n 2
2 t1 1, n g n 1 5 n 2
t 2 0 , n 1 2 t1 1, n g n 1 5 n 2
4. t 2 0 , n 1 t 2 0 , n 1 n t 3 8 , n 18
Proof
t 2
2 0 , n1 t 2 0 , n1 1 8 1 6 1 8
2
1 8 n 1 7 n n 1 8
t 2 0 , n 1 t 2 0 , n 1 n t 3 8 , n 18
5. The following triples are in arithmetic progression
a) t , t , t
1 9 , n 2 0 , n 2 1, n
Proof
b) t , t , t
2 0 , n 2 1, n 2 2 , n
t
1 2 2
1 9 , n t 2 1, n 1 7 n 1 5 n 1 9 n 1 7 n
2
2
2 9 n 8 n
t1 9 , n t 2 1, n 2 t 2 0 , n
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