✔ Subtract the first term from the second term to find d.
Q2. Which formula represents the nth term of an AP?
✔ The standard formula includes subtracting one from the position number.
Q3. Find the 3rd term if a=2 and d=3.
✔ Substitute values into a + (n-1)d to get 2 + 2(3) = 8.
Show transcript
[Slide 1] Understanding Arithmetic Progressions
An arithmetic progression adds the same number every time. Think of climbing stairs where each step is equal height. We need a shortcut to find any step without counting all.
[Slide 2] The nth Term Formula
This formula connects the first term and the common difference. Multiply the difference by one less than the term number. Add this result to the starting value.
[Slide 3] Worked Example Setup
Let us find the twentieth term of this specific sequence. The first number is three and we add four each time. We will substitute these values into our formula.
[Slide 4] Solving the Example
Plugging in twenty for n gives us nineteen times four. Multiply nineteen by four to get seventy-six. Finally, add three to seventy-six to get the answer.
[Slide 5] Avoiding Common Errors
Students often forget to subtract one from the term number. This leads to calculating the next term instead of the current one. Always check your subtraction before multiplying.
[Slide 6] Quick Recap Summary
Remember the formula links position to value using constant steps. Practice finding terms quickly for your board exams. You now have the tool to solve these problems.