Find x and y, given that 1,x and y are in arithmetic sequence, and 1,y,x are in geometric sequence
Find the first three terms of a geometric sequence given that the sum of the first four terms is 21 2/3 and the sum to infinity is 27.
The three numbers a,b and c, whose sum is 15, are successive terms of a geometric sequence, and b, a and c are successive terms of an arithmetic sequence. Find the values of a, b and c
Thank you so much for help given on these questions
Hello, christina!
Here's the second one . . .
Find the first three terms of a geometric sequence,
given that the sum of the first four terms is and the sum to infinity is 27.
.[1]
.[2]
Divide [1] by [2]: . .
Substitute into [2]: .
Therefore, the first three terms are: .
Hello again, christina!
And here's the last one . . . and there are three solutions.
The three numbers , whose sum is 15,
are successive terms of a geometric sequence,
and are successive terms of an arithmetic sequence.
Find the values of
In the geometric series, the numbers are represented like this:
. .
In the arithmetic series, the same numbers are represented like this:
. .
The common difference is the difference between consecutive terms:
. . . .
Equate and : .
. .
If , we have a trivial sequence: .
We have: . .[3]
If , we have another trivial sequence: .
[3] becomes: .
If , we have: .
And we have a third solution: .