The number of terms of a geometric sequence is even.
- The sum of the odd terms, that is - terms in the odd places (First term + Third Term + Fifth Term + ... and so on) is 4329
- The sum of the even terms, that is – terms in the even places (Second Term + Fourth Term + Sixth Term + ... and so on) is 5772
- The last term exceeds the first by 2343
Determine the geometric sequence.
(In reply to Solution
I have solved this puzzle by "guided guessing" as follows: <br>
Since each even-placed member is q times the previous (odd-placed ) member, q = 5771/4329 = 4/3.<br>
So it wasreasonable to assume that the 1st member is a*3^k, then a*(3^(k-1))*4, a*(3^(k-2))*4^2, a*(3^(k-2))*4^3, etc<br>
Looking at tne numbers given 243 was too small to start with, so I SELECTED a=1,k=6 and got:<p>
729; 972; 1,296; 1,728; 2,304; 3,072. - the true results.<br><br>
Truly, nothing warrants an integer a, but it seemed logical to me
as a 1st choice, and it worked...