Identify patterns in sequences, and study arithmetic progressions where each term increases by a constant difference.
A sequence is an ordered list of numbers following a pattern. Recognizing the pattern lets us predict future terms.
Find the next term: 2, 5, 8, 11, ...
14 (each term adds 3)
Find the next term: 1, 4, 9, 16, ...
25 (these are perfect squares: 1²,2²,3²,4²,5²)
An arithmetic progression (AP) has a constant common difference between consecutive terms. The nth term is aₙ=a+(n−1)d.
Find the 8th term of the AP 4, 9, 14, 19, ...
a=4, d=5; a₈=4+7×5=39
Is the sequence 3, 6, 12, 24 an AP? Explain.
No, the differences are 3,6,12 — not constant, so it's not an AP (it's actually a GP)
1. Find the next term: 5, 10, 15, 20, ...
2. Find the next term: 1, 1, 2, 3, 5, 8, ...
3. Find the 10th term of the AP 7, 12, 17, 22, ...
4. Is the sequence 2, 4, 8, 16 an AP?
5. Find the common difference of the AP where the 3rd term is 11 and the 1st term is 3.
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