Find the 6th Term: Completing the Sequence 3, _, 27, _, 243, ?

Q: What are the missing terms in positions 2 and 4?

Position 2: $ 3 × 3 = 9 $Position 4: $ 27 × 3 = 81 $So the complete sequence is: 3, 9, 27, 81, 243, 729

Q: How can I double-check my answer for the 6th term?

Use the formula: $ a_n = a_1 × r^{(n-1)} $For the 6th term: $ a_6 = 3 × 3^5 = 3 × 243 = 729 $Or count up: 3 → 9 → 27 → 81 → 243 → 729

Q: What if I can't see the pattern right away?

Start by dividing consecutive given terms: $ 27 ÷ 3 = 9 $ and $ 243 ÷ 27 = 9 $. Since there's one missing term between each, the common ratio is $ \sqrt{9} = 3 $!

Geometric Sequences with Missing Terms

Look at the sequence below:

$3,\text{?,}27,\text{?,}243,\text{?}$

What is the 6th element of the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 6th term in the sequence

00:03 Let's observe the change between terms

00:10 We can see that each term equals 3 raised to the position (N)

00:13 Let's deduce the next terms from the pattern

00:16 Let's calculate and substitute

00:20 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

Look at the sequence below:

$3,\text{?,}27,\text{?,}243,\text{?}$

What is the 6th element of the series?

Final Answer

$729$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify the common ratio by dividing consecutive terms
Technique: From 3 to 27: $27 ÷ 3 = 9$ , so multiply by 3 twice
Check: Verify each term: $3 × 3^5 = 3^6 = 729$ ✓

Common Mistakes

Avoid these frequent errors

Assuming the sequence adds the same number each time
Don't treat this as an arithmetic sequence by adding a constant difference = wrong pattern! The terms 3, 27, 243 multiply by powers of 3, not add. Always check if consecutive terms have the same ratio (geometric) or difference (arithmetic).

Practice Quiz

Test your knowledge with interactive questions

Look at the following set of numbers and determine if there is any property, if so, what is it?

$$ 94,96,98,100,102,104 $$

FAQ

Everything you need to know about this question

How do I know this is a geometric sequence and not arithmetic?

Look at the pattern! From 3 to 27 is ×9, and from 27 to 243 is also ×9. In arithmetic sequences, you add the same number. In geometric sequences, you multiply by the same number.

Why is the common ratio 3 and not 9?

Great observation! We jump by 9 from one given term to the next, but there's a missing term in between. So we multiply by 3 twice: $3 × 3 = 9$ and $9 × 3 = 27$ .

What are the missing terms in positions 2 and 4?

Position 2: $3 × 3 = 9$
Position 4: $27 × 3 = 81$
So the complete sequence is: 3, 9, 27, 81, 243, 729

How can I double-check my answer for the 6th term?

Use the formula: $a_n = a_1 × r^{(n-1)}$
For the 6th term: $a_6 = 3 × 3^5 = 3 × 243 = 729$
Or count up: 3 → 9 → 27 → 81 → 243 → 729

What if I can't see the pattern right away?

Start by dividing consecutive given terms: $27 ÷ 3 = 9$ and $243 ÷ 27 = 9$ . Since there's one missing term between each, the common ratio is $\sqrt{9} = 3$ !

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