Good evening Sirs and Madams,
I would just like to consult these two problems that I encountered in my textbook. I am quite frustrated since i can't figure both of these questions as I was reviewing for my exams. If you are kind enough to help and guide me, I'd thank you with all my heart. (I am having a feeling that a kind of question like this will appear in my exam on tuesday)
Let X1, X2, X3, .... Xk be an Arithmetic Sequence and Y1, Y2, Y3, ...Ykbe a Geometric Sequence.
Define the sequence Z1, Z2, Z3, ....Zkby Zk = Xk + Yk for every K element of Natural numbers.
If Z1=1, Z2=8, Z3=32, Find Z5.
Let S0 be a square whose side has length of 1 unit.
Let S1 be the square whose vertices are the midpoints of the sides of S0. (connecting the midpoint of consecutive sides)
Let S2 be the square whose vertices are the midpoints of the sides of S1, and so on.
We do this infinitely many times to obtain squares Sk where K is a Natural number.
If ASk denotes the AREA of square Sk, Find AS1 + AS2 + AS3 + ... + ASk.