Question

445n2 +56

Answer 1

The n th term of the sequence is given as,

a n =n n 2 +5 4 (1)

Substitute n=1 in equation (1),

a 1 =( 1 ) ( 1 ) 2 +5 4 = 1+5 4 = 6 4 = 3 2

Substitute n=2 in equation (1),

a 2 =( 2 ) ( 2 ) 2 +5 4 = 4+5 2 = 9 2

Substitute n=3 in equation (1),

a 3 =( 3 ) ( 3 ) 2 +5 4 =( 3 ) 9+5 4 =( 3 ) 14 4 = 21 2

Substitute n=4 in equation (1),

a 4 =( 4 ) ( 4 ) 2 +5 4 =16+5 =21

Substitute n=5 in equation (1),

a 5 =( 5 ) ( 5 ) 2 +5 4 =( 5 ) 25+5 4 =( 5 ) 30 4 = 75 2

Therefore, the required first five terms of the sequence are,

3 2 , 9 2 , 21 2 ,21, 75 2 .