the product of fifth term seventh term and ninth term of a geometric sequence is 27 find the 7th term
Answers
Answer:
A geometric sequence has a constant ratio (common ratio) between consecutive terms.
For 3, 9, 27, ... the common ratio is 3 because:
3 X 3 = 9
9 X 3 = 27
So to find the 7th term you can do it two ways:
One way:
3 is the 1st term, 9 is the 2nd term, 27 is the 3rd term so then
4th term: 27 X 3 = 81
5th term: 81 X 3 = 243
6th term: 243 X 3 = 729
7th term: 729 X 3 = 2,187
Another way:
You can use the explicit formula
a
n
=
a
1
⋅
r
n
−
1
, where
a
n
is the nth term,
a
1
is the first term, n is the number of the term, and r is the common ratio
so
a
7
=
3
⋅
3
7
−
1
a
7
=
3
⋅
3
6
a
7
=
3
⋅
729
a
7
=
2
,
187
Both ways get you to the same
Step-by-step explanation:
Answer:
fifth term = ar^(5-1) = ar^4
seventh term = ar^(7-1) = ar^6
ninth term = ar^(9-1) = ar^8
Multiplying fifth, seventh and ninth terms:
ar^4 * ar^6 * ar^8 = 27
or, a^3 * r^18 = 27
or, ( ar^6 )^3 = 3^3
or, ( ar^6) = 3
Since ar^6 is the seventh term, and ar^6 = 3, we can say that the seventh term is 3.