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Sequences and the nth Term
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
Each number is a term, and its position is n. Finding a formula for the nth term lets you jump straight to any term.
The coefficient of n always equals d. In 5, 8, 11, 14 the difference d = 3 and a = 5, so the nth term is 3n + 2.
In 3, 6, 12, 24 the ratio r = 2. The 5th term is 3 × 2^4 = 48. If |r| < 1 the terms shrink.
Gauss paired 1+100, 2+99, … to add 1..100 in seconds: 50 pairs of 101 = 5050. That is Sn = (n/2)(first + last).
Hard words & meanings
| sequence | an ordered list of numbers following a definite rule |
| term | a single number in a sequence, identified by its position n |
| nth term | a formula in n that gives the value at any position |
| arithmetic progression | a sequence with a constant difference between consecutive terms |
| common difference | the fixed amount d added each step in an AP |
| geometric progression | a sequence with a constant ratio between consecutive terms |
| common ratio | the fixed multiplier r in a GP |
| sum of terms | the total of the first n terms, written Sn |
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