arithematic sequence chapter 1 , 10th standard, Important concepts

Important concepts

Arithematic sequence

1. Sequences and its algebra

2. The relation between common difference, terms and position of terms
⋆ The difference between two terms of an arithematic sequence will be the
product of the difference between their positions and its common difference
⋆ xm − xn = (m − n)d

3. The algebra of an arithmetic sequence is always in the form an + b.Here ais the
common difference and a + b is the first term.

4. The terms of an arithmetic sequence leaves the same remainder on dividing by the common difference

5. When p times common difference is added to nth term of an arithmetic sequence
we get (n + p)th term
xn + pd = x
                    (n+p)
For example, x5 + 6d = x11, x20 + 10d = x30

6. The sum of some natural numbers from 1 is half the product of natural number at the end and its successor
                    n(n + 1)
                          2

7. The sum of first n terms of an arithmetic sequence having algebraic form is
          sn = a×n(n + 1) + bn
                           2

8. If an arithmetic sequence has odd number of terms the middle term will be half of the sum of the terms

9. The sum of some numbers forming an arithmetic sequence will be half the sum
of first and last number in the sequence