Sequences & series (GP)
Geometric progressions, their sums, and AM and GM.
Learn with Kutty
Go one screen at a time. Press Next when you are ready. Tap 🔊 Read to me to listen.
In a GP you multiply by the same number every time.
Look: Start at 3, multiply by 2 each time.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1r for 81, 27, 9…?
2Next term: 5, 10, 20, __
31 + ½ + ¼ + ⅛ + … adds up to?
! Careful!
✗Adding 4 each time for 2, 6, 18.
✓It multiplies by 3.
✗Adding forever when r = 2.
✓Only a shrinking GP (r between −1 and 1) has a total.
See the whole lesson on one page
In a GP you multiply by the same number every time.
Start with a, multiply by r each time. If r is a fraction (like ½), the terms shrink, and adding them all up for ever still gives a finite total.
Think of it like thisA message forwarded to 2 friends, who each forward it to 2 more… 1, 2, 4, 8, 16. It multiplies by 2 each time.
- r
- The number you multiply by.
Solved together
What is the 6th term of 2, 6, 18, …?
Each term is 3 times the one before: r = 3.
Keep multiplying.
2, 6, 18, 54, 162, 486
AnswerThe 6th term is 486.
For older learners and grown-ups: a little more
nth term aₙ = a·rⁿ⁻¹. Sum of n terms Sₙ = a(rⁿ − 1)/(r − 1). Sum to infinity (|r| < 1): a/(1 − r).
Now practise it
Kanakku makes new questions on sequences & series (gp) every time. It shows the working and gives a hint when you are stuck.