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The recursive formula to describe a sequence is shown below

a1=4
an=an-1+2n

State the first four terms of this sequence.

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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.

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