Learn with Amar
Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Derive a term formula from the first term and common difference.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
An arithmetic sequence begins 7,11,15,19. Find its twentieth term.
Why this math matters
Translate regularly increasing or decreasing counts into an indexed rule. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Index an arithmetic sequence correctly
PausedQuestion: Start with the question. Paused.
Question
Start with the question
An arithmetic sequence begins 7,11,15,19. Find its twentieth term.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
First term a₁=7; difference d=4
The constant increase is four.
Develop the calculation
aₙ=7+4(n−1)
Reaching term n requires n−1 jumps after the first term.
Check and interpret
a₂₀=7+4(19)=83
Using twenty jumps would overshoot to the twenty-first term.
The result
a₂₀=7+4(19)=83
Using twenty jumps would overshoot to the twenty-first term.
Common mistakes to catch
- Check whether indexing starts at zero or one.
- The number of steps after the first term is n−1.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find the twelfth term of 20,17,14,… with a constant difference.
Show a hint
Use d=−3 and eleven jumps.
Reveal answer and explanation
−13
20−3(11)=−13.
Practice 2
If aₙ=5n+2 for n≥1, what are the first term and common difference?
Show a hint
Evaluate n=1 and compare neighboring terms.
Reveal answer and explanation
First term 7; difference 5
The coefficient gives the gap, while the constant alone is not the first term under this indexing.
Take the idea with you
Translate regularly increasing or decreasing counts into an indexed rule.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Count repeated factors in a geometric sequence
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