2006-09-08 19:25:42 · 5 answers · asked by free aung san su kyi forthwith 2 in Science & Mathematics ➔ Mathematics
1+2+4=7
2+4+8=14
4+8+16=28
8+16+32=56
This series yields multiples of 7, so GP cannot mean powers of consecutive integers.
if GP means 2^x, 2^y, and 2^z are consecutive integers, then
282/3=94
93+94+95 =282
2^x=93
ln(2^x)=ln(93)
xln2=ln93
x=ln93 / ln2
x=6.539
y=6.555
z=6.570
2006-09-08 20:51:01 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
sheesh this is long...i've been workin on this for the past fifteen mins and i've lost my patience...
btw peeps..GP stands for GEOMETRIC PROGRESSION ...
since 2^x, 2^y and 2^z are in gp,
2^z / 2^y=2^y / 2^x -->> eq. 1
sum of a finite gp = a(1-r^n)/1-r where a is the first term, r=common ratio and n=total no. of terms (studied dis a long time ago..i hope the formula's rite! )
now frm eq. 1 u have 2 common ratios, so u can get 2 more equations by substituting the both the values of r in the sum formula
(remember n=3)
282 = 2^x(1-(2^z/2^y)^3)/1-(2^z/2^y) ---->> eq. 2
282 = 2^x(1-(2^y/2^x)^3)/1-(2^y/2^x) ---->> eq.3
soo um there u go...u got 3 eqs...with 3 variables x, y and z...u shud be able to find them out now....u just gotta solve them...sorry the solving was taking too much time...that's where i lost my patience...but the method's right...hopefully!
hav a gr8 day!
2006-09-09 02:59:00 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I don't think you can get 282 with integer values of x,y,z. Did you mean the sum is 292? Because 2^2 + 2^5 + 2^8 =
4 + 32 + 256 = 292
2006-09-09 02:32:37 · answer #3 · answered by Aaron 2 · 0⤊ 0⤋
GP?? Are you asking about a Galois Partition?
Doug
2006-09-09 02:32:57 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋
what is a gp?
2006-09-09 02:30:51 · answer #5 · answered by bob b 1 · 0⤊ 0⤋