Question

The recursive formula to describe a sequence is shown below

a1=4
an=an-1+2n

State the first four terms of this sequence.

Answer 1

Given that the recursive formula for a sequence is
`a_n=a_(n-1)+2n`

The first term of the sequence is
`a_1=4`

We need to determine the first four terms of the sequence.

Second term:

The second term of the sequence can be determined by substituting n = 2 in the recursive formula.

Thus, we have;

`a_2=a_(2-1)+2(2)`

`a_2=a_(1)+2(2)`

`a_2=4+4`

`a_2=8`

Thus, the second term of the sequence is 8.

Third term:

The third term of the sequence can be determined by substituting n = 3 in the recursive formula.

Thus, we have;

`a_3=a_(3-1)+2(3)`

`a_3=a_(2)+2(3)`

`a_3=8+6`

`a_3=14`

Thus, the third term of the sequence is 14.

Fourth term:

The fourth term of the sequence can be determined by substituting n = 4 in the recursive formula.

Thus, we have;

`a_4=a_(4-1)+2(4)`

`a_4=a_(3)+2(4)`

`a_4=14+8`

`a_4=22`

Thus, the fourth term of the sequence is 22.

Hence, the first four terms of the sequence is 4, 8, 14, 22.