# Thread: Finding the radius of a cylinder

1. ## Algebra

Hello,
can any "smart" person who is very good at math solve this question? it is (d) in the attachment....
good luck
thanks

2. $S_n$ is defined by $S_n= \frac{1}{6}n(n+1)(n+2)$ so $S_{n-1}= \frac{1}{6}(n-1)((n-1)+ 1)((n-1)+ 2)= \frac{1}{6}(n-1)(n)(n+1)$

You could multiply both of those out and subtract but it is simpler to notice that each has factors of 1/6, n, and n+1 andfactor those out:
$S_{n}- S_k{n-1}= \frac{1}{6}(n)(n+1)(n+2- (n-1))= \frac{1}{6}n(n+1)(3)$

3. ## sequence oroblem

Originally Posted by igcsestudent
Hello,
can any "smart" person who is very good at math solve this question? it is (d) in the attachment....
good luck
thanks
sequence 1,4,10,20,35 Find nextterm
Differences 3,6,10, 15, next difference is 21 6 comes after 3,4,5
35+21 is 56

bjh

4. cool!
thanks really appreciate your help!