Asked by Safiya
The term of a G. P is 9 and the fifth term is 16.find the fourth term.
Answers
Answered by
oobleck
which term is 9?
If it's the 3rd (I think I saw this problem earlier) then
r^2 = 16/9
so r = ±4/3
now you can find desired term.
or, just take the geometric mean: √(9*16) = 12
If it's the 3rd (I think I saw this problem earlier) then
r^2 = 16/9
so r = ±4/3
now you can find desired term.
or, just take the geometric mean: √(9*16) = 12
Answered by
mathhelper
The term of a G. P is 9 ?????
Did you mean the first term is 9 ? I will assume that.
so a = 9
9r^4 = 16
r^4 = 16/9
r^2 = ± 4/3
if r^2 = 4/3
r = ± 2/√3
if r^2 = - 4/3
r would be a complex number. Usually in the study of sequences,
we are restricted to real numbers.
so the fourth term = ar^3 = 9(2/√3)^3 = 9(8/3√3) = 24/√3
or 9(-2/√3)^3 = -24/√3
check: if a = 9, r = 2/√3
sequence is
9, 18/√3, 12, 24/√3, 16, ...... looks good
Did you mean the first term is 9 ? I will assume that.
so a = 9
9r^4 = 16
r^4 = 16/9
r^2 = ± 4/3
if r^2 = 4/3
r = ± 2/√3
if r^2 = - 4/3
r would be a complex number. Usually in the study of sequences,
we are restricted to real numbers.
so the fourth term = ar^3 = 9(2/√3)^3 = 9(8/3√3) = 24/√3
or 9(-2/√3)^3 = -24/√3
check: if a = 9, r = 2/√3
sequence is
9, 18/√3, 12, 24/√3, 16, ...... looks good
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.