Arithmetic progressions
Number patterns that grow by the same amount: nth term and sum.
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In an AP you add the same number every time.
Look: Start at 3, add 4 each time.
✏️ Your turn!
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1d for 20, 17, 14…?
210th term of 2, 5, 8…?
31 + 2 + … + 100 = ?
! Careful!
✗Week 20 = 50 + 20 × 20.
✓Only 19 jumps: 50 + 19 × 20.
✗Finding d as earlier minus later.
✓d = later − earlier.
See the whole lesson on one page
In an AP you add the same number every time.
Start at a. Add d each time. The 20th term is a plus 19 jumps of d. To add them all up, pair the first with the last.
Think of it like thisClimbing stairs: each step takes you up the same height. Step 20 is 19 steps above step 1.
- a
- The first term.
- d
- The jump each time.
Solved together
Ravi saves ₹50 in week 1, ₹70 in week 2, ₹90 in week 3… How much in week 20?
Start a = 50. Jump d = 20.
Week 20 is 19 jumps after week 1.
50 + 19 × 20 = 50 + 380 = 430
Answer₹430 in week 20.
For older learners and grown-ups: a little more
nth term: aₙ = a + (n − 1)d. Sum: Sₙ = n/2 × (first + last). Ravi’s total for 20 weeks: 10 × (50 + 430) = ₹4,800.
Now practise it
Kanakku makes new questions on arithmetic progressions every time. It shows the working and gives a hint when you are stuck.