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.