Find the 5th Term in the Sequence: 10, 20, 40, ...

Q: How do I know if it's multiplying or adding?

Check the differences and ratios! If differences are equal (20-10=10, 40-20=20), it's adding. If ratios are equal (20÷10=2, 40÷20=2), it's multiplying.

Q: What if the ratio isn't a whole number?

That's totally fine! Geometric sequences can have any constant ratio - like 0.5, 1.5, or even negative numbers. Just multiply consistently.

Q: Can I use a formula instead of listing all terms?

Yes! For geometric sequences, use $ a_n = a_1 \times r^{n-1} $ where r is the ratio. Here: $ a_5 = 10 \times 2^{5-1} = 10 \times 16 = 160 $

Q: What if I get confused about which term I'm looking for?

Always count carefully! Term 1 is 10, Term 2 is 20, Term 3 is 40, Term 4 is 80, Term 5 is 160. Use your fingers or write it out step by step.

Q: How can I double-check my pattern is right?

Test with the first few given terms! Calculate what the pattern predicts and see if it matches. If 10×2=20 and 20×2=40 match the sequence, you've got it right!

Geometric Sequences with Common Ratios

Look at the sequence below:

$10,20,40,\text{?,?,?}$

What is the 5th element of the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the fifth term in the sequence.

00:13 Notice how each term changes from the one before it.

00:20 Use this pattern to figure out the next terms.

00:24 Now, calculate and replace the numbers.

00:39 And that's how we find the answer 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:

$10,20,40,\text{?,?,?}$

What is the 5th element of the series?

Step-by-step solution

To solve this problem, we need to determine the pattern in the sequence $10, 20, 40, \text{?,?,?}$ .

The terms of the sequence seem to be generated by multiplying by a common ratio of 2. This is characteristic of a geometric sequence.

The first term $a_1 = 10$ .

The second term is $a_2 = a_1 \times 2 = 10 \times 2 = 20$ .

The third term is $a_3 = a_2 \times 2 = 20 \times 2 = 40$ .

Following the pattern of multiplying by 2, we can determine the next terms:

The fourth term $a_4 = a_3 \times 2 = 40 \times 2 = 80$ .
The fifth term $a_5 = a_4 \times 2 = 80 \times 2 = 160$ .

Thus, the 5th element of the sequence is $160$ .

Final Answer

$160$

Key Points to Remember

Essential concepts to master this topic

Pattern: Each term equals previous term times constant ratio
Technique: Multiply by 2: 10 → 20 → 40 → 80 → 160
Check: Verify ratio consistent: 20÷10 = 2, 40÷20 = 2, 80÷40 = 2 ✓

Common Mistakes

Avoid these frequent errors

Adding the same amount instead of multiplying
Don't add 10 to each term (10, 20, 30, 40...) = arithmetic sequence pattern! This gives wrong answers because the sequence doubles, not adds. Always identify if terms multiply or add by the same amount.

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 it's multiplying or adding?

Check the differences and ratios! If differences are equal (20-10=10, 40-20=20), it's adding. If ratios are equal (20÷10=2, 40÷20=2), it's multiplying.

What if the ratio isn't a whole number?

That's totally fine! Geometric sequences can have any constant ratio - like 0.5, 1.5, or even negative numbers. Just multiply consistently.

Can I use a formula instead of listing all terms?

Yes! For geometric sequences, use $a_n = a_1 \times r^{n-1}$ where r is the ratio. Here: $a_5 = 10 \times 2^{5-1} = 10 \times 16 = 160$

What if I get confused about which term I'm looking for?

Always count carefully! Term 1 is 10, Term 2 is 20, Term 3 is 40, Term 4 is 80, Term 5 is 160. Use your fingers or write it out step by step.

How can I double-check my pattern is right?

Test with the first few given terms! Calculate what the pattern predicts and see if it matches. If 10×2=20 and 20×2=40 match the sequence, you've got it right!

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