Posted by suma on Saturday, August 3, 2013 at 7:19am.
The sum of second term and fourth term of G.P is 30 and difference between sixth term and second term is 90,how to find third term

math  Reiny, Saturday, August 3, 2013 at 9:05am
first term  a
common ratio  r
The sum of second term and fourth term of G.P is 30 > ar + ar^3 = 30
ar(1 + r^2) = 30 , #1
difference between sixth term and second term is 90 > ar^5  ar = 90
ar(r^4  1) = 90 , #2
divide #2 by #1
(r^4  1)/(1+r^2) = 3
(r^2 + 1)(r^2  1)/(1+r^2) = 3
r^2  1 = 3
r^2=4
r = ±2
in #1
if r = 2
2a(1+4) = 30
10a=30
a=3
if r=2
2a(1+4) = 30
a = 3
third term = ar^2
= 12 or 12
check:
for a=3, r=2
sequence is 3 6 12 24 48 96
sum of 2nd and fourth = 6+24 = 30
diff between 6th and 2nd = 96  6 = 90
for a=3, r=2
sequence is 3 6 12 24 48 96
same as above, the negative terms don't enter the picture.
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