iGCSE (2021 Edition)

# 9.06 Infinite geometric series

## Interactive practice questions

What condition must be satisfied by an infinite geometric series in order for its sum to exist?

the absolute value of the common ratio must be less than $1$1

A

the common ratio must be negative

B

the common ratio must be less than $1$1

C

the common ratio must be greater than $1$1

D

the absolute value of the common ratio must be greater than $1$1

E

the absolute value of the common ratio must be less than $1$1

A

the common ratio must be negative

B

the common ratio must be less than $1$1

C

the common ratio must be greater than $1$1

D

the absolute value of the common ratio must be greater than $1$1

E
Easy
Less than a minute

Consider the infinite geometric sequence $11$11, $22$22, $44$44, $88$88, $\text{. . .}$. . .

Consider the infinite geometric sequence $3$3, $-12$12, $48$48, $-192$192, $\text{. . .}$. . .

Consider the infinite geometric sequence $-40$40, $-20$20, $-10$10, $-5$5, $\text{. . .}$. . .

### Outcomes

#### 0606C12.5

Use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression.