Thread: Another geometric series

Please help...

the sum of the first n terms of a positive geomtetric sequence is 315 and the sum of the 5th 6th and 7th term is 80640. identify the sequence.

I have no idea how to find a, or r. thanks xxx

Sn=a(1-r^n)
------1-r
Un= ar^(n-1) (i think off the top of my head)

315=a(1-r^n)
-------1-r

5th term:
U5=ar^4
U6=ar^5
U7=ar^6
so

80640=ar^4 + ar^5 + ar^6

80640=ar^4(1-r^3)
----------1-r
Hopefully by solving the simultaneous equation you can get a and r, then go back to your original equation (with 315) to find n

Hello, mathshelpneeded!

There must be a typo . . .
As stated, there is no unique solution.
. . There are three variables and only two equations.

I believe that the "n" is a "3" . . .

The sum of the first 3 terms of a positive geometric sequence is 315
and the sum of the 5th, 6th and 7th term is 80,640.
Identify the sequence.

The sum of the first 3 terms is: .a + ar + ar² .= .315

The sum of the 5th, 6th and 7th terms is: .ar^4 + ar^5 + ar^6 .= .80,640


. . Factor the first equation: .a(1 + r + r²) .= .315 .[1]

Factor the second equation: .ar^4(1 + r + r²) .= .80,640 .[2]

. . . . . . . . . . . . . .ar^4(1 + r + r²) . . .80,640
Divide [2] by [1]: . ------------------- .= .--------
. . . . . . . . . . . . . . .a(1 + r + r²) . . . . . 315

. . And we have: .r^4 = 256 . → . r = 4


Substitute into [1]: .a(1 + 4 + 4²) .= .315 . → . a = 15


The sequence is: .15, 60, 240, 960, 3,840, 15,360, 61,440, ...