I. The common ratio = 900/36 = 25
II. The first term = 36 - 25 = 11
The second term of a geometric progression is 36 more than the first term.the difference between the 4th and 3th terms is 900. Calculate
I. The common
II. The first term
2 answers
As is the case in most of these type of problems, the bot is wrong
ar - a = 36 or a(r-1) = 36
ar^3 - ar^2 = 900 or ar^2(r-1) = 900
divide those two equations:
r^2 = 900/36 = 25
r = ± 5
if r = 5, 4a = 36, a = 9
if r = -5, -6a = 36, a = -6
check:
if r = 5, a = 9, your terms are 9, 45, 225, 1125, 5625, ...
notice that 2nd - first = 45-9 = 36
and that 4th - 3rd = 1125-225 = 900
if r = -5, a= -6, your terms are -6, 30, -150, 750, -37504500
notice that 2nd - 1st = 30-(-6) = 36
and that 4th - 3rd = 750-(-150) = 900
ar - a = 36 or a(r-1) = 36
ar^3 - ar^2 = 900 or ar^2(r-1) = 900
divide those two equations:
r^2 = 900/36 = 25
r = ± 5
if r = 5, 4a = 36, a = 9
if r = -5, -6a = 36, a = -6
check:
if r = 5, a = 9, your terms are 9, 45, 225, 1125, 5625, ...
notice that 2nd - first = 45-9 = 36
and that 4th - 3rd = 1125-225 = 900
if r = -5, a= -6, your terms are -6, 30, -150, 750, -37504500
notice that 2nd - 1st = 30-(-6) = 36
and that 4th - 3rd = 750-(-150) = 900
2 answers