Arithmetic Sequence: Finding December's Food Price in 30→33→36 Pattern

Q: How do I know this is definitely an arithmetic sequence?

Check if the difference between consecutive terms is constant. Here: 33-30=3, 36-33=3, 39-36=3. Since all differences equal 3, it's arithmetic!

Q: Can I use the arithmetic sequence formula instead of adding repeatedly?

Absolutely! Use $ a_n = a_1 + (n-1)d $ where a₁ = 30, d = 3, and n = 12 for December: $ a_{12} = 30 + (12-1)(3) = 63 $

Q: Why does the problem show some months filled in and others blank?

This tests your understanding of arithmetic sequences. The given values establish the pattern, and you use that pattern to find the missing December value.

Q: Could the food prices follow a different pattern?

The consistent difference of $ +3 $ each month clearly shows it's arithmetic, not geometric or quadratic. Always verify the pattern type before solving!

Arithmetic Sequences with Monthly Price Patterns

The series describes the price of a meal in a food chain from January to December.

$30, 33, 36, 39, 42, 45 , \\48 , \underline{\phantom{88}}, \underline{\phantom{88}}, \underline{\phantom{88}},\underline{\phantom{88}},\boxed{\underline{\phantom{88}}}$

How much does food cost in December?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the meal price in December

00:04 Find the difference between each term

00:07 This is the pattern of the sequence

00:18 Calculate the missing terms according to the pattern we found

00:55 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

The series describes the price of a meal in a food chain from January to December.

$30, 33, 36, 39, 42, 45 , \\48 , \underline{\phantom{88}}, \underline{\phantom{88}}, \underline{\phantom{88}},\underline{\phantom{88}},\boxed{\underline{\phantom{88}}}$

How much does food cost in December?

Step-by-step solution

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

Step 1: Calculate the Common Difference.
Step 2: Determine Prices for Missing Months.

Now, let's work through each step:
Step 1: Common Difference Calculation:
Observe the pattern from January ( $30$ ) to July ( $48$ ).
Calculate the common difference: $d = 33 - 30 = 3$ .
This confirms each month increases by $3$ .
Step 2: Find the Price for December:
Starting from July ( $48$ ):

August: $48 + 3 = 51$
September: $51 + 3 = 54$
October: $54 + 3 = 57$
November: $57 + 3 = 60$
December: $60 + 3 = 63$

Therefore, the solution to the problem is $63$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify the common difference by subtracting consecutive terms
Technique: Add d = 3 repeatedly: 48 + 3 + 3 + 3 + 3 + 3 = 63
Check: Count positions: December is 12th month, verify using formula $a_{12} = 30 + 11(3) = 63$ ✓

Common Mistakes

Avoid these frequent errors

Counting months incorrectly or starting from wrong position
Don't assume July is the 6th term when it's actually the 7th month = off-by-one errors! This shifts all calculations and gives wrong final answers. Always match each given value to its correct month position first.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

How do I know this is definitely an arithmetic sequence?

Check if the difference between consecutive terms is constant. Here: 33-30=3, 36-33=3, 39-36=3. Since all differences equal 3, it's arithmetic!

Can I use the arithmetic sequence formula instead of adding repeatedly?

Absolutely! Use $$ a_n = a_1 + (n-1)d $$ where a₁ = 30, d = 3, and n = 12 for December: $a_{12} = 30 + (12-1)(3) = 63$

What if I made an arithmetic error while adding?

Double-check by working backwards! Start from your December answer and subtract 3 repeatedly to see if you get back to July's price of 48.

Why does the problem show some months filled in and others blank?

This tests your understanding of arithmetic sequences. The given values establish the pattern, and you use that pattern to find the missing December value.

Could the food prices follow a different pattern?

The consistent difference of $$ +3 $$ each month clearly shows it's arithmetic, not geometric or quadratic. Always verify the pattern type before solving!

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