Question

formulae of progressions

Answer 1

These are the formulae of arithmetic progressions:-

1.   a n = a 1 + ( n − 1 ) d

 2.   a n = a m + ( n − m ) d

 3. S n = n 2 [ 2 a 1 + ( n − 1 ) d ]

 4. S n = n 2 ( a 1 + a n )

  5. n ¯  = S n / n

 6. n ¯ = a 1 + a n 2


where

If

a 1  is the first term of an arithmetic progression.

a n is the nth term of an arithmetic progression.

 d  is the difference between terms of the arithmetic progression.

n is the number of terms in the arithmetic progression.

S n  is the sum of n terms in the arithmetic progression.

n ¯  is the mean value of arithmetic series.