Arithmetic Sequence:-

The sequence in which each consecutive terms has a same common difference.

Eg:-0, 2, 4, 6, 8,...

->a is the first term of the sequence, d is the common difference and n is no. of terms

->To find the nth term of AP:an = a+(n-1)*d

->To find the sum of the AP: Sn = (n/2)*[2a + (n-1)*d]

= (n/2)*[a + {a + (n-1)*d}] [: expression in angular bracket is an]

= (n/2)*(af+al)

->Hence, the sum of AP can also be written as: Sn = (n/2)*(af+al) [:af=first term & al=last term]

Geometric Sequence:- ====================

The sequence in which each consecutive term has a common ratio.

Eg:-1, 5, 25, 125,...

->a is the first term of the sequence, r is the common ratio and n is no. of terms

->To find the nth term of GP:an = (a * r^(n-1))

->To find the sum of the GP: Sn = a * {[r^(n-1)-1]/[r-1]}

Harmonic Sequence:- ===================

The sequence in which the reciprocal of each term forms an arithmetic sequence.

Eg:-(1/2),(1/4),(1/6),(1/8),...

Summation for Harmonic Sequence:

->a is the first term of the sequence, d is the common difference and n is no. of terms

->To find the nth term of AP:an = {1 / [a+b*(n-1)]}