Question

1. Determine the next term of the following sequence: 0, 3,8,15...

1.1. What is the eleventh term of this sequence? Show all your working.

1.2. Name the type of numbers formed by the numbers added in the sequence.

Answer 1

Let $a_n$ be the $n$ -th element of the sequence: $0,3,8,15,…$

Then $a_n=n^2-1$

$a_1=1^2-1=0$

$a_2=2^2-1=3$

$a_3=3^2-1=8$

$a_4=4^2-1=15$

1.The next term is $a_5=5^2-1=24$ ,

1.1 The eleventh term of this sequence is $a_{11}=11^2-1=121-1=120$ , $a_{11}=120$

1.2 $a_{n+1}-a_n=((n+1)^2-1)-(n^2-1)=n^2+2n+1-1-n^2+1=2n+1$

Type of numbers: odd numbers.