Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 5: Arithmetic Progressions — notes
The chapter’s 5 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Patterns and what an AP is
Okay, so, look around you.
- • Term: each number in the list
- • AP: each term = preceding term + fixed number
- • Fixed number = common difference (d)
- • d can be positive, negative or zero
- • Example: 8000, 8500, 9000, ... (d = 500)
2. General form and finding a and d
Okay, so look at the board.
- • General AP: a, a+d, a+2d, a+3d, ...
- • Check: is ak+1 − ak same every time?
- • Example: 4, 10, 16, 22, ...
- • 10-4 = 6, 16-10 = 6, 22-16 = 6, so d = 6
- • Next terms: 22+6 = 28, 28+6 = 34
3. The nth term of an AP
Okay, so let's think about Reena's salary again.
- • an = a + (n − 1) d
- • Example: AP 2, 7, 12, ...
- • a = 2, d = 5, n = 10
- • a10 = 2 + (10-1)×5
- • a10 = 2 + 45 = 47
4. Finding which term equals a given value
Okay, so sometimes you're given a term's value, and you have to find which term number it is.
- • AP: 21, 18, 15, ...
- • a = 21, d = -3
- • -81 = 21 + (n−1)(-3)
- • -105 = -3n, so n = 35
- • 35th term is − 81; 8th term is 0
5. Sum of the first n terms of an AP
Okay, so think of Shakila.
- • Sn = (n/2)[2a + (n−1)d]
- • Also: Sn = (n/2)(a + an) = (n/2)(a + l)
- • Example: a = 100, d = 50, n = 21
- • S = (21/2)[200 + 1000]
- • S = (21/2) × 1200 = 12600
Summary
So, let's look back at everything we did in this chapter. We started with simple things — Reena's salary, the rungs of a ladder. Both had a pattern. Each term was made from the one before it, by adding a fixed number. We called that fixed number the common difference, d. And a list like that, we called an Arithmetic Progression. So the general form looked like a, a+d, a+2d, and so on. Now, how do we check if a list is an AP? We check if a sub (k+1) − a sub k stays the same every time. If it does, it's an AP. Then we found something very useful — the nth term formula, an = a + (n−1)d. This lets us find any term directly. It also lets us work backwards — if we're given a term's value, we can find which term it is. After that, we learned how to add up the terms of an AP quickly, without adding one by one. That's the formula Sn = (n/2)[2a + (n−1)d]. And if we already know the last term, l, we can also write it as Sn = (n/2)(a + l). Remember how we used this for Shakila's money box? Her savings added up to ₹12600 by her 21st birthday. Tell me — which of these two sum formulas would you use if you don't know the last term?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 5. Written from the textbook, checked twice.
Questions parents and students ask
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