Question

Consider this sequence

1(8-7), 2(10-8), 3(12-9), 4(14-10), ........, ........ .
(i) Write down the next term and the 10th term of this sequence in the form a(b-c) where a, b and c are integers.
(ii) Write down the nth term in the form a(b-c) and then simplify your answer.

Answer 1

Hello,


`u_(1) =1*(8-7)=1*(2*4-(6+1))\\ u_(2) =2*(10-7)=2*(2*5-(6+2))=2*(2*(4+1)-(6+2))\\ u_(3) =3*(12-9)=3*(2*6-(6+3))=3*(2*(4+2)-(6+3))\\ u_(4) =4*(14-10)=4*(2*7-(6+4))=4*(2*(4+3)-(6+4))\\`



`u_(10)=10*(2*(4+10)-(6+10))\\ =10*(28-16)`


`...\\\\ u_(n) =n*(2*(n+n-1)-(6+n))\\ =n*(4n-2-6-n)=n(3n-8)\\`