Identify which of the following are geometric sequences.
For those that are, write down the first term and the common ratio.
Did this page help you?
Identify which of the following are geometric sequences.
For those that are, write down the first term and the common ratio.
Did this page help you?
Write down a formula for the th term of each of the following geometric sequences
Did this page help you?
Find the 5th and 10th terms in each of the following geometric sequences
Did this page help you?
The first term of a geometric progression is 6.
The sum to infinity of the progression is 8.
Show that the common ratio of the progression is 0.25.
For a geometric progression with first term 6 and common ratio 0.25, briefly explain why the sum to infinity will exist.
Did this page help you?
The 3rd and 6th terms of a geometric sequence are 10 and 270 respectively,
Find the first term and the common ratio.
The 12th term of a geometric sequence is 16 times greater than the 8th term.
Find the possible values of the common ratio.
Did this page help you?
Find the sum of the first 12 terms of the geometric series that has first term 5 and common ratio , giving your answer to the nearest whole number.
Find the sum to infinity of the geometric series that has first term 4 and common ratio .
Did this page help you?
The first term of a geometric sequence is 2.
The 6th term of the sequence is 486.
The sum of the first terms is 177 146.
Find the common ratio.
Show that
Did this page help you?
Given that the sum to infinity of the progression exists, show that the sum to infinity is .
Given that the sum to infinity is , find the value of .
Did this page help you?
The th term of a geometric progression is given by .
Write down the first five terms of the progression.
Calculate the sum of the first five terms of the progression.
Did this page help you?
The first three terms of a geometric sequence are given by , , and respectively, where
Show that .
Find the value of the 15th term of the sequence.
State, with a reason, whether 8192 is a term in the sequence.
Did this page help you?
The sum of the first two terms in a geometric series is 9.31.
The sum of the first four terms in the same series is 11.02.
The common ratio of the series is .
Show that .
Hence find the two possible values of .
Did this page help you?
The first term of a geometric series is , and its common ratio is 5. A different geometric series has first term and common ratio 3. The sum of the first three terms of both series is the same.
Find the value of , giving your answer as a fraction in simplest terms.
Did this page help you?
The first three terms in a geometric series are , , , where is a constant.
Find the common ratio, , of this series.
Find the sum of the first 12 terms in this series.
Did this page help you?
The first three terms of a geometric progression are , and . Given that the sum to infinity of the progression exists
write down an inequality that the common ratio of the progression must satisfy, and hence find the range of possible values of
find an expression for the sum to infinity of the progression in terms of .
Did this page help you?
A geometric progression has first term 64, and the sum to infinity of the progression is 384.
Show that the common ratio, , of the progression is .
Find the difference between the ninth and tenth terms of the progression, giving your answer correct to 3 significant figures.
Calculate the sum of the first eight terms of the progression, giving your answer correct to 3 significant figures.
Given that the sum of the first terms of the progression is greater than 380, show that
Did this page help you?
The th term of a geometric progression is given by .
Calculate, giving your answers as exact values
The sum of the first nine terms of the progression.
The sum to infinity of the progression starting from the tenth term.
Did this page help you?
The first three terms of a geometric sequence are given by , , and respectively, where is a non-zero real number.
Find the value of the 102nd term in the sequence.
Did this page help you?
The sum of the first three terms in a geometric series is 8.75.
The sum of the first six terms in the same series is 13.23.
Find the common ratio, , of the series.
Did this page help you?
A geometric series has first term and common ratio .
Show that the sum of the first ten terms of the series is equal to , where is a positive integer to be determined.
Did this page help you?
The first three terms in a geometric series are , , , where is a constant.
Find the value of .
Find the sum of the first 12 terms in this series.
Did this page help you?
The second and fifth terms of a geometric series are 13.44 and 5.67 respectively. The series has first term and common ratio .
By first determining the values of and , calculate the sum to infinity of the series.
Calculate the difference between the sum to infinity of the series and the sum of the first 20 terms of the series. Give your answer accurate to 2 decimal places.
Did this page help you?
A geometric progression has first term 9, and the sum of the first three terms of the series is 19. The common ratio of the series is .
Show that .
Find the two possible values of .
Given that the sum to infinity of the progression exists, find the sum to infinity of the progression.
Did this page help you?
The th term of a geometric progression is given by .
Calculate, giving your answers as exact values
The sum to infinity of the progression starting with the seventh term.
The sum to infinity of the progression whose th term is given by , where is defined as above.
Did this page help you?
The first three terms of a geometric sequence are given by , , and respectively, where is a non-zero real number.
Find the value of the sixth term in the sequence, giving your answer as a fraction.
Did this page help you?
The sum of the first four terms in a geometric series is 27.2, and the sum of the first eight terms in the same series is 164.9.
Given that the first term of the series is positive, find the common ratio, , of the series.
Did this page help you?
A geometric series has first term , and its terms are connected by the relationship for all .
Given that all the terms of the series are positive, show that the sum of the first twelve terms of the series may be written in the form
where and are positive integers and is a surd.
Did this page help you?
The first three terms in a geometric progression are , , , where is a constant.
Find the possible values of .
Given that the sum to infinity of the progression exists, find the sum to infinity of the series progression.
Did this page help you?
The second and third terms of a geometric progression are and , where is a real number not equal to 1 or -1.
Given that the sum to infinity of the progression exists,
Find the range of possible values of .
Given that the sum to infinity of the series is -6,
find the two possible values of .
Did this page help you?
The geometric progression is defined by , where denotes the term of the progression. The sum to infinity of the progression exists and is denoted by . The first term of the progression is , and the common ratio is .
A different progression is formed by squaring all the terms of the progression above.
Show that is also a geometric progression, and that its sum to infinity also exists.
The sum to infinity of the progression T is .
Express the ratio in terms of and , simplifying your answer as far as possible.
Show that if , then for all . Comment on what this shows about the relationship between the terms of the two progressions.
Did this page help you?
The th term of a geometric progression is given by
Calculate the sum of the eleventh through twenty-third terms of the sequence whose th term is given by where is defined as above. You should give your answer as an exact value.
Did this page help you?