Question

A recursive definition of an arithmetic sequence is shown below:

a1=7
an=an−1+3
Which of the following expressions represents the nth term of this sequence?
A. n+3
B. 3n+4
C. 3n+7
D. 7n+3

Answer 1

The nth term of the arithmetic sequence can be expressed as 7 + 3n.

Step-by-step explanation:

The recursive definition of an arithmetic sequence is given as:

a1 = 7

an = an-1 + 3

To find the nth term of this sequence, we can use the recursive definition to generate the terms.

Starting with a1 = 7, we can calculate the subsequent terms:

• a2 = a1 + 3 = 7 + 3 = 10
• a3 = a2 + 3 = 10 + 3 = 13
• a4 = a3 + 3 = 13 + 3 = 16

From this pattern, we can see that the nth term of this sequence is given by the expression 7 + 3n.