Question

write down the general form of A.p

Answer 1

Arthematic progression

Answer 2

The general form of an Arithmetic Progress is {a, a + d, a + 2d, a + 3d, a + 4d, a + 5d, ..........}, where ‘a’ is known as the first term of the Arithmetic Progress and ‘d’ is known as the common difference (C.D.).

If a is the first term and d is the common difference of an Arithmetic Progress, then its nth term is a + (n - 1)d.

Let a11, a22, a33, a44, ........, ann, .................. be the given Arithmetic Progress. Then a11 = first term = a

By the definition, we have

a22 - a11 = d

⇒ a22 = a11 + d

⇒ a22 = a + d

⇒ a22 = (2 - 1)a + d:

a33 - a22 = d

⇒ a33 = a22 + d

⇒ a33 = (a + d) + d

⇒ a33 = a + 2d

⇒ a33 = (3 - 1)a + d:

a44 - a33 = d

⇒ a44 = a33 + d

⇒ a44 = (a + 2d) + d

⇒ a44 = a + 3d

⇒ a44 = (4 - 1)a + d:

a55 - a44 = d

⇒ a55 = a44 + d

⇒ a55 = (a + 3d) + d

⇒ a55 = a + 4d

⇒ a55 = (5 - 1)a + d:

Similarly, a66 = (6 - 1)a + d:

a77 = (7 - 1)a + d:

ann = a + (n - 1)d.

Therefore, nth term of an Arithmetic Progress whose first term = ‘a’ and common difference = ‘d’ is ann = a + (n - 1)d.