A sequence is defined by the recurrence relation u(n+1) = 1/3 u(n) + 10 with u(3) = 6 . Find the value of u(4) and the limit of the sequence.

A sequence is defined by the recurrence relation un+1 = 1/3 un + 10  with u3 = 6 . Find the value of u4 and the limit of the sequence.

To find the value of u4 we replace un by u3 in the equation and then calculate un+1

u4 = 1/3 u3 + 10

u4 = 1/3 x 6 + 10

u4 = 2 + 10

u4 = 12

To find the limit of the series we have to find for which value un+1 is equal to un .

Let's call this value x . Then we have:

x = 1/3 x + 10

We can subtract 1/3 x on both sides to get:

x - 1/3 x = 10

2/3 x = 10

Now we multiply by 3 and then divide by 2:

x = 10 x 3 / 2

x = 15

The limit of the sequence is 15.

David-Ruben S. GCSE Physics tutor, A Level Physics tutor, IB Physics ...

6 months ago

Answered by David-Ruben, a GCSE Physics tutor with MyTutor

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


£18 /hr

Edward B.

Degree: Medical Sciences (Bachelors) - Leeds University

Subjects offered:Physics, Geography+ 3 more

English Language
-Personal Statements-

“University of Leeds student offering tuition in Biology, Geography, Physics and English Language”

MyTutor guarantee

Kirsty M. A Level Maths tutor, GCSE Maths tutor, 13 Plus  Maths tutor...
£20 /hr

Kirsty M.

Degree: Computer Science (Bachelors) - St. Andrews University

Subjects offered:Physics, Maths+ 2 more


“ABOUT ME I am a computer science student at the University of St Andrews, and have always been enthusiastic about maths and science, to such an extent that I am a STEM ambassador, a title given to people who encourage school pupils to ...”

£20 /hr

Jonathan P.

Degree: Physics (Masters) - Durham University

Subjects offered:Physics, Maths


“About Me: I am a Physics student at Durham University. My passion is physics, and by association maths, I will aim to instil asimilar passion in students during my tutorials. I am a highly patient and approachable individual.  I have...”

About the author

David-Ruben S.

Currently unavailable: for new students

Degree: Mathematical Physics (Masters) - Edinburgh University

Subjects offered:Physics, Maths+ 1 more


“Hello, my name is David, I’m studying Mathematical Physics at the University of Edinburgh. I have been studying in Edinburgh for 3 years. I’m from Germany, I’ve always liked to go and live abroad, to make new experiences and meet peop...”

MyTutor guarantee

You may also like...

Posts by David-Ruben

A sequence is defined by the recurrence relation u(n+1) = 1/3 u(n) + 10 with u(3) = 6 . Find the value of u(4) and the limit of the sequence.

Find the equation of the line passing through the point ( 2, −3) which is parallel to the line with equation y + 4x = 7

Other GCSE Physics questions

What is teminal velocity?

How deep is the water if it takes a pulse of ultrasound 0.8s to be received back at the boat. the speed of ultrasound is 1600m/s in water

Can you define current, potential difference and resistance in a circuit, and give their units?

On a day with no wind, a large object is dropped from a tall building. The object experiences air resistance during its fall to the ground. State and explain, in terms of the forces acting, how the acceleration of the object varies during its fall.

View GCSE Physics 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