Arithmetic & Geometric Series (Edexcel IGCSE Further Pure Maths): Exam Questions

The th term of a geometric series is

Find the sum to infinity of this series.

Give your answer in the form where and are integers to be found.

Expand in ascending powers of up to and including the term in

and simplifying each term as far as possible.

Write down the range of values of for which this expansion is valid.

Hence, using your expansion with a suitable value for , obtain an approximation to decimal places of

Show that

Hence, or otherwise, evaluate

The sum of the first and second terms of a geometric series is

The sum of the second and third terms of is

Show that the common ratio of is

Show that the first term of is

Find the sum to infinity of

The sum to terms of is

Find, using logarithms, the least value of such that

The sum of the fifth, sixth and seventh terms of an arithmetic series is nine times the sum of the first and second terms.
The third term of is 12

Find the first term and common difference of

The th term of is

Find the value of

The sum to terms of is

Given that

find the value of

A geometric series has first term and common ratio
The third term of is 9 and the sum to infinity of is 192

Show that

A geometric series has first term and common ratio
The third term of is 9 and the sum to infinity of is 192

Given that is a rational number

write down the value of

A geometric series has first term and common ratio
The third term of is 9 and the sum to infinity of is 192

show that =144

The sum to terms of is

Using logarithms, find the least value of such that

Show that

Hence, or otherwise, evaluate

The th term of a convergent geometric series is

Find the sum to infinity of the series.

Give your answer in the form where and are integers to be found.

A geometric series with common ratio , has first term 16 and third term

Find the two possible values of

Given that

find the sum to infinity of

The sum to terms of is greater than 33

Find, using logarithms, the least possible value of
Show your working clearly.

The sum to terms of an arithmetic series is

The sum of the first four terms of is 42 and the fifth term of is 23

Show that where and are prime numbers.

where is the th term of

Find the value of

The th term of an arithmetic series is where

and

Find

The term of a geometric series is

The first three terms of are given by

Find the possible values of

Given that is convergent with sum to infinity 250

find the value of