Geometric Progression

What is progression?

• it happening or developing gradually or in stages.

• a sequence of numbers in which each term is related to its predecessor by a uniform law

• a law of mathematical induction

• none of the above

Which of the following is considered as type of progression?

• Arithmetic

• Geometric

• Cyclic

• Articulic

What is the common ratio for this geometric progression?

48, 24, 12, 6, ........

• 2

• $\frac{1}{2}$

• 3

• $\frac{1}{3}$

Find the 7th term of the geometric progression
2,  $\frac{2}{3}$   ,  $\frac{2}{9}$  ,  $\frac{2}{27}$  , …

•  $\frac{2}{4374}$  

•  $\frac{2}{1458}$  

•  $\frac{2}{729}$  

•  $\frac{2}{2187}$  

 $1+4+16+64+.................$  
Find  $S_8$  

• 16382.5

• 16383.5

• 20845

• 21845

 $24+12+6+3+........$  
Find  $S_{\infty}$  

• 48

• 58

• 148

• 158

 $5,\ 10,\ 20,\ ..........$  
Find r

• 2

• 4

• 5

• 10

The sequence 0.02, 0.04, 0.08, …... is not geometric progression.

• True

• False

 $p,\ p^3,\ p^5\ ,\ ........$  
Arithmetic or Geometric Progression?

• Arithmetic Progression

• Geometric Progression

Which of the following are true?

•  $S_n=\frac{a\left(1-r^n\right)}{1-r},\ \left|r\right|<1$  
  

•  $S_n=\ \frac{a\left(r^n-1\right)}{r-1},\ \left|r\right|>1$  

•  $S_n=\frac{a\left(1-r^n\right)}{1-r},\ \left|r\right|>1$  

•  $S_n=\ \frac{a\left(r^n-1\right)}{r-1},\ \left|r\right|<1$