C2 Series Exam Question Help

vv2006

The question is

The nth term of an arithmetic sequence is un = 90-3n

a. find u1 and u2 done

b. Write down the common difference of the arithmetic sequence done

c. Given that k
sigma un = 0
n=1

find the value of k

(stuck!)

Reply 1

Swayum

They mean "Find when the sum from n = 1 up to k equals 0 for un"

Sum = k/2(2a + d(k-1))
k/2(2a + d(k-1)) = 0
2ak + dk^2 -dk = 0

Plug in a as u1, d as the difference and you'll have a quadratic in k.

Reply 2

Rabite

Well.
Let's sum it all up.
Sn = S{90-3n} = S(90) - 3S(n) =0
S(constant) = n(constant)
and S(n)=½n(n+1)
Use those results :p:

Alternatively, we can write
Sum(AP) = ½n(a+L) =0
Where L is the last term and a is the first.
Either way, you end up solving a quadratic.

[edit] Oh, those 'n's should really be 'k's, but you get the point.

I can elaborate if you want ~