What an AP is
Add the same thing every time
An arithmetic progression is a list where each term after the first is the previous term plus a FIXED number.
↳ Same step, every time.
📚 Chapter Learning Kit
Arithmetic Progressions · Class 10 Mathematics
English 3 topics 169 leveled MCQs 60 flashcards 3 games Free
Shared by a Veda teacher · Generated with Veda AI · Sep 2026
⚡ Veda Bites
💡 Key Idea
➗ Formula
➗ Formula
➗ Formula
💡 Key Idea
⚠️ Common Mistake
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The common difference
Later minus earlier
↳ Reversing it flips the sign.
The general form
Every AP looks like this
↳ The multiplier is always one less than the position.
The nth term
Any term, one line
↳ It reaches the 100th term without writing the other 99.
Why n − 1
The first term is free
You start AT $a_1$, so it costs no steps.
↳ That is the whole reason for the minus one.
a + nd
The error that looks right
Using $a + nd$ gives the term AFTER the one asked for.
↳ Always $(n-1)$, never n.
📖 Smart notes
What you'll study, topic by topic
1
What an Arithmetic Progression Is
An arithmetic progression is a list of numbers in which every term after the first is made by adding the SAME fixed number to the one before it. That fixed number is the common difference, and testing for it — by subtrac…
- An AP is a list where each term after the first is the previous term PLUS a fixed number.
- That fixed number is the COMMON DIFFERENCE, written d.
- $d = a_{k+1} - a_k$ — always the later term MINUS the earlier one.
~40 min · full explanation, examples & memory tricks in the app
2
The nth Term of an AP
One formula, $a_n = a + (n-1)d$, reaches any term of an AP without writing out the ones before it. The same formula run backwards answers the other standard questions: which term a given number is, how many terms a finit…
- The nth term is $a_n = a + (n - 1)d$, where a is the first term and d the common difference.
- The multiplier is $n - 1$ because the first term needs NO step: reaching the nth term takes $n-1$ steps.
- $a_1 = a$, $a_2 = a + d$, $a_{10} = a + 9d$.
~45 min · full explanation, examples & memory tricks in the app
3
Sum of the First n Terms of an AP
Pairing the first term with the last, the second with the second-last, and so on gives every pair the same total — which is how the whole sum collapses to $S_n = \frac{n}{2}[2a + (n-1)d]$. When the last term is known, th…
- $S_n = \frac{n}{2}\left[2a + (n - 1)d\right]$ — use this when a and d are known.
- $S_n = \frac{n}{2}(a + l)$ — use this when the LAST term l is known.
- The second form is the first with $l = a + (n-1)d$ substituted in; they always agree.
~50 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
169 questions laddered from warm-up to topper-level, each with an explanation. A taste:
An arithmetic progression is a list in which each term after the first is the previous term
Beginner
A times a fixed number
B squared
C plus a fixed number
D halved
Show answer & explanation
plus a fixed number
Adding a fixed amount is exactly the definition.
The fixed number added each time is called the
Beginner
A common ratio
B common difference
C first term
D arithmetic mean
Show answer & explanation
common difference
It is written d and is the same at every step.
For the AP $3, 8, 13, 18, \ldots$, the common difference is
Beginner
A −5
B 3
C 8
D 5
Show answer & explanation
5
$8 - 3 = 5$.
For the AP $20, 17, 14, 11, \ldots$, the common difference is
Beginner
A 3
B −3
C 20
D −20
Show answer & explanation
−3
$17 - 20 = -3$; later minus earlier.
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