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
The term of a G. P is 9 and the fifth term is 16.find the fourth term.
2 answers
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
2 answers