Arithmetic Progression & Geometric Progression

1. 3) Formula Method of Finding Roots
The quadratic equations which cannot
be solved through the method of
factorization can be solved with the
help of a formula

2. Example: Solve 5x2 + 6x + 1 = 0
Soln: Here Coefficients are: a = 5, b = 6, c =
1
Quadratic Formula: x =
−b ± (b2 − 4ac)
2𝑎
Putting the values of a, b and c, we get:
x =
−6 ± (62 − 4x5x1)
2∗5

3. x =
−6 ± (36− 20)
10
x =
−6 ± (16)
10
x =
−6 ± 4
10
x = −0.2 or −1

4. Arithmetic Progression ( A.P.) & Geometric
progression (G.P.)
Arithmetic Progression ( A.P.): In a sequence if the
difference between any term and its preceding
term (tn+1−tn) is constant, then the sequence is
called an Arithmetic Progression ( A.P.)
Consider the following sequences
1) 2, 5, 8, 11, 14, …
2) 4, 10, 16, 22, 28, …
are in Arithmetic Progression ( A.P.)

5. Geometric progression (G.P.):
In a sequence if the ratio between any term
and its preceding term (tn+1/tn) is constant,
then the sequence is called an Geometric
Progression ( G.P.).
Hence a G.P. can also be written as a, ar,
a𝑟2
, a𝑟3
, ....
where a is first term and r is common
ratio.

6. Examples :
i) 2, 4, 8, 16, .... [here a = 2, r = 2]
ii) 3, 9, 27, .... [a = 3, r =3]
are in G.P.

7. THANK YOU