# geometric sequence question

• Jul 25th 2008, 06:35 PM
cityismine
geometric sequence question
The first term of a geometric sequence is 27, and the sixth term is 512/9.

Find the seventh term.

Find the sum of the first five terms of this sequence.

My answers are 66.03 and 185.95, am I right?
• Jul 25th 2008, 10:18 PM
Chop Suey
Yes, you are correct. :-)
• Jul 25th 2008, 10:48 PM
cityismine
Thanks for the confirmation, cause the answer in the book is different. Another typo!
• Jul 26th 2008, 04:24 AM
Soroban
Hello, cityismine!

I suspect the typo is in the statement of the problem . . .

Quote:

The first term of a geometric sequence is 27, and the sixth term is 1024/9

(a) Find the seventh term.

(b) Find the sum of the first five terms of this sequence.

(a) Formula: .a(n) .= .a(1)·r^{n-1}

We have: .a(1) = 27, . a(6) = 1024/9

Then: .a(6) = a(1)·r^5 . . 1024/9 = 27r^5 . . r^5 = 1024/243

. . Hence: .r .= .4/3

Therefore: .a(7) .= .a(6)·r .= .(1024/9)(4/3) .= .4096/27

. . . . . . . . . . . . . . . . . . . r^n - 1
(b) Formula: .S(n) .= .a(1)·---------
. . . . . . . . . . . . . . . . . . . . r - 1

. . . . . . . . . . . . . . .(4/3)^5 - 1 . . . 781
Hence: . S(5) .= .27·-------------- .= .-----
. . . . . . . . . . . . . . . . 4/3 - 1 . . . . . .3

Were those the answers they expected?

• Jul 26th 2008, 10:09 AM
cityismine
Yes sir, those are the answers in the book.