Limits

dds001 wrote:If K1=200
Kn=200+0.2Kn-1
What will K20 be closest to?
a)230
b)240
c)250
d)280
e)300

I know the answer is c, [but is there a quick way to working out the solution without manually calculating the first few values, ie values for K1, K2, K3, etc

The problem with these is you have to get at least the first 2 to confirm a pattern. The third would be to really make sure you are not taking any risk.

200
200 + .2(200)=200(1.2) (This is the hardest part. Resisting the temptation NOT to add so you can discover some pattern). Since you want the fastest way we are going to hope that the 20% increase between the first and 2nd term will continue some pattern: that is 1/5 is a geometric ratio.

So we have geometric sequence of the form 200(1/5)^n where a is 200 and r =1/5. Since r<1, we use to find sum a/1-r

200/(1-1/5)=250