Question

Identify the 9th term of the given arithmetic sequence: 5, 9, 13, 17, 21, ...

a) 41
b) 37
c) 45
d) 33

Answer 1

Using the arithmetic sequence formula, the 9th term of the sequence 5, 9, 13, 17, 21, ... is calculated to be 37.

Step-by-step explanation:

The student asked to identify the 9th term of the arithmetic sequence: 5, 9, 13, 17, 21, .... To find this, we need to determine the common difference and use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where a1 is the first term, d is the common difference and n is the term number. In this sequence, the common difference is 4 (9 - 5).

Now, we will calculate the 9th term (n = 9):

1. Plug the values into the formula: a9 = 5 + (9 - 1) × 4.
2. Perform the calculation: a9 = 5 + 8 × 4.
3. Multiply: a9 = 5 + 32.
4. Add: a9 = 37.

Therefore, the 9th term of the sequence is 37, which corresponds to option (b).