Revision: Algebra >> Sequence and Series Mathematics ISC (Commerce) Class 11 CISCE

When the numbers (terms) in a sequence are connected to each other by a positive (plus) sign or a negative (minus) sign, the sequence becomes a series. 

A progression is a sequence where each term follows a uniform rule.

• Every progression is a sequence, but with a clear pattern.

A sequence is a group of numbers arranged in a definite order following a rule.

• Numbers in a sequence are called terms or elements.

• The term at position n is called the nth term, denoted by Tₙ.

An Arithmetic Progression (A.P.) is a sequence in which the difference between consecutive terms is constant.

• Common difference = d = second term − first term

• The general form of an AP is a, a + d, a + 2d, a + 3d, …
  a = first term
  d = common difference

A sequence, in which each of its terms can be obtained by multiplying or dividing its preceding term by a fixed quantity, is called a geometric progression.

• A fixed number is called the common ratio (r)

G.M. between a and b

G² = ab 

G =\[\sqrt{ab}\]

G is the geometric mean between a and b.

• Three terms in A.P.

  a − d,  a,  a + d​

• Four terms in A.P.

  a − 3d,  a − d,  a + d,  a + 3d​

• Five terms in A.P.

  a − 2d,  a − d,  a,  a + d,  a + 2d​

• Six terms in A.P.

  a − 5d,  a − 3d,  a − d,  a + d,  a + 3d,  a + 5d