Arithmetic Sequence Problem: Find the 7th Term in 51, 47, 43, 39, ...

Q: How do I know if the common difference is positive or negative?

Look at the pattern! If the numbers get smaller as you go from left to right, the common difference is negative. If they get larger, it's positive.

Q: Can I just keep subtracting 4 until I reach the 7th term?

Yes! That's actually a great way to double-check your answer. Start with 51 and subtract 4 six times: 51 → 47 → 43 → 39 → 35 → 31 → 27.

Q: Why do we use (n-1) in the formula instead of just n?

Because the first term doesn't need any 'jumps' - it's already there! You only need (n-1) jumps to get from the 1st term to the nth term.

Q: What happens if I use the wrong common difference?

You'll get completely wrong answers! Always double-check by calculating the difference between at least 2-3 pairs of consecutive terms to make sure it's consistent.

Arithmetic Sequences with Negative Common Differences

Assuming that the sequence continues with the same rule, what number appears in the 7th element?

$51,47,43,39\ldots$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 7th term

00:08 This is the sequence formula

00:11 Substitute the desired position in the formula and solve

00:19 Always solve multiplication and division before addition and subtraction

00:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Assuming that the sequence continues with the same rule, what number appears in the 7th element?

$51,47,43,39\ldots$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the pattern of the sequence.
Step 2: Use the pattern to find the 7th term.
Step 3: Verify the solution with the formula for arithmetic sequences.

Now, let's work through each step:

Step 1: Identify the pattern.
The given sequence is $51, 47, 43, 39, \ldots$ . Calculating the difference between consecutive terms:

$47 - 51 = -4$
$43 - 47 = -4$
$39 - 43 = -4$

The common difference $d$ is $-4$ .

Step 2: Use the pattern to find the 7th term.
We know the sequence is arithmetic with the first term $a_1 = 51$ and common difference $d = -4$ . Using the formula for the $n$ -th term of an arithmetic sequence:

a_n = a_1 + (n-1) \times d

For the 7th term ( $n = 7$ ):

a_7 = 51 + (7-1) \times (-4) = 51 + 6 \times (-4) = 51 - 24 = 27

Step 3: Verify.
Confirmed pattern and arithmetic calculation yield the same result.

Therefore, the solution to the problem is $27$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Calculate differences between consecutive terms to find common difference
Formula Application: Use $a_n = a_1 + (n-1) \times d$ where d = -4
Verification: Check by continuing the sequence: 51, 47, 43, 39, 35, 31, 27 ✓

Common Mistakes

Avoid these frequent errors

Adding the common difference instead of subtracting
Don't add 4 each time just because you see the number 4 = wrong increasing sequence! The common difference is -4, not +4, because each term gets smaller. Always pay attention to whether the sequence increases or decreases.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

How do I know if the common difference is positive or negative?

Look at the pattern! If the numbers get smaller as you go from left to right, the common difference is negative. If they get larger, it's positive.

What if I lose track of which term I'm looking for?

Always count carefully: 51 (1st), 47 (2nd), 43 (3rd), 39 (4th), and so on. The position number is your 'n' value in the formula.

Can I just keep subtracting 4 until I reach the 7th term?

Yes! That's actually a great way to double-check your answer. Start with 51 and subtract 4 six times: 51 → 47 → 43 → 39 → 35 → 31 → 27.

Why do we use (n-1) in the formula instead of just n?

Because the first term doesn't need any 'jumps' - it's already there! You only need (n-1) jumps to get from the 1st term to the nth term.

What happens if I use the wrong common difference?

You'll get completely wrong answers! Always double-check by calculating the difference between at least 2-3 pairs of consecutive terms to make sure it's consistent.

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