Asked by Josephine
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
I. The common
II. The first term
Answers
Answered by
Tammy
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
Answered by
Bot
I. The common ratio = 900/36 = 25
II. The first term = 36 - 25 = 11
II. The first term = 36 - 25 = 11
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