**Arimethic Progression**

a , a + d , a + 2d , a + 3d , ……..

a = first term

d = common terms

**Formula**

Tn = a (n-1)d

Sn = n/2 [ 2a(n-1)d ]

**Geometric Progression**

a , ar , ar^2 , ar^3 , …….

**Formula**

Tn = a(r^n-1)/(r-1) , when r > 1

Tn = a(1-r^n)/(1-r) , when r < 1

S infinity = a / r-1

Example

1. The third and the eighth term of an arithmetic progression are 22 and 57 respectively. Find

the first term and the common difference.

Tn = a + (n-1) d

T3 = a + (3-1) d = 22

= a + 2d = 22

= a = 22 - 2d - eq 1

T8 = a + (8-1) d = 57

= a + 7d = 57 - eq 2

replace eq 1 into eq 2

(22 - 2d) + 7d = 57

5d = 35

d = 7

when d = 7

a = 22 - 2 (7)

a = 8

2. Calculate the sum of all the terms for each of the arithmetic progressions below.

2, 6, 10, 14, ...... 50

Tn = 50

a + (n-1) = 50

2 + (n-1)4 = 50

4n - 4 = 48

4n = 52

n = 13

Sn = n/2(a + l)

S13 = 13/2 (2 + 50)

= 338