The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

Note here: u_n indicates u subscript n.

(a) u_1 = 48 and the ratio, r = 0.6

Using a calculator, u_2 = 48 x 0.6 = 28.8

u_3 = 28.8 x 0.6 = 17.28

(b) We have the known result that the sum to infinity of a geometric series is a/(1-r) where a is the first term and r is the common ratio.

Therefore, the sum to infinity here is 48/(1-0.6) = 48/0.4 = 120

(c) We now want the sum from the fourth term to infinity. We can use the same formula as before, but replacing the first term which we called a with the fourth term of the sequence.

Calculating the fourth term: u_4 = 17.28 x 0.6 = 10.368

Therefore, our sum is equal to 10.368/(1-0.6) = 10.368/0.4 = 25.92

Felix S. IB Maths tutor, 11 Plus Maths tutor, GCSE Maths tutor, 13 pl...

12 months ago

Answered by Felix, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Eleanor J.

Degree: Natural Sciences in Maths and Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“Study Maths and Physics at Durham Previous tutoring experience Enjoy helping students improve and enjoy the subjects Adaptable to different academic needs”

£20 /hr

Liam M.

Degree: Mathematics (Bachelors) - St. Andrews University

Subjects offered:Maths, Science+ 2 more


“I have a real passion for Maths and Physics and would relish the opportunity to pass this passion on to others! ”

£22 /hr

Samuel J.

Degree: Physics (Masters) - Manchester University

Subjects offered:Maths, Physics


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

About the author

Felix S.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“About me: Hi, I'm Felix and I'm currently studying for a Mathematics degree at Warwick University. I am very keen to show people not just how to pass maths exams, but how to actuallyenjoy the subject too! I got A* in GCSE Maths and th...”

You may also like...

Posts by Felix

Express 0.545454... as a fraction in its simplest form.

Given a^2 < 4 and a+2b = 8. Work out the range of possible values of b. Give your answer as an inequality.

Prove that the function f:ZxZ -> ZxZ defined by f(x,y) = (2x+y,x+y) is a bijetion.

Sunita has 75 pens and she ties them into bundles of 8. How many pens does she have left over?

Other A Level Maths questions

what is implicit differentiation and how is it achieved?

How do I differentiate y=x^x?

What are the roots of 3x^2 + 13x + 4 ?

The curve "y=6x-x^2" and the line "y=2x" intersect at the origin. At what other coordinate to they intersect?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss