Question

what is the 6th term of the arithmetic sequence: 4, 9, 14, 19, ...? 29 39 34 24

Explanation:

Step1: Identify the common difference

In an arithmetic sequence, the common difference \( d \) is found by subtracting consecutive terms.
\( d = 9 - 4 = 5 \), \( d = 14 - 9 = 5 \), \( d = 19 - 14 = 5 \). So \( d = 5 \).

Step2: Use the arithmetic sequence formula

The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term, \( n \) is the term number, and \( d \) is the common difference.
Here, \( a_1 = 4 \), \( d = 5 \), and we want the 6th term, so \( n = 6 \).
Substitute the values into the formula:
\( a_6 = 4 + (6 - 1) \times 5 \)

Step3: Calculate the 6th term

First, calculate \( (6 - 1) \times 5 = 5 \times 5 = 25 \).
Then, \( a_6 = 4 + 25 = 29 \). Wait, no, wait, let's check again. Wait, the 4th term is 19. Let's list the terms:
1st term: 4
2nd term: \( 4 + 5 = 9 \)
3rd term: \( 9 + 5 = 14 \)
4th term: \( 14 + 5 = 19 \)
5th term: \( 19 + 5 = 24 \)
6th term: \( 24 + 5 = 29 \)? Wait, no, wait, 19 (4th) +5=24 (5th), 24 +5=29 (6th). Wait, but let's use the formula again. \( a_n = a_1 + (n - 1)d \). So \( a_6 = 4 + (6 - 1) \times 5 = 4 + 25 = 29 \). Wait, but the options have 29, 39, 34, 24. Wait, but when we list the terms:
1:4, 2:9, 3:14, 4:19, 5:24, 6:29. So the 6th term is 29? Wait, but let's check the formula again. Wait, \( a_1 = 4 \), \( n = 6 \), \( d = 5 \). So \( a_6 = 4 + (6 - 1)*5 = 4 + 25 = 29 \). But wait, the 5th term is 24, 6th is 29. But let's check the options. One of the options is 29. Wait, but let's do it step by step by adding 5 each time:
Term 1: 4
Term 2: 4 + 5 = 9
Term 3: 9 + 5 = 14
Term 4: 14 + 5 = 19
Term 5: 19 + 5 = 24
Term 6: 24 + 5 = 29
Yes, so the 6th term is 29.

Answer:

29