top button
Flag Notify
    Connect to us
      Facebook Login
      Site Registration Why to Join

    Get Free Puzzle Updates

Facebook Login
Site Registration

What is this geometric sequence? Sum of first few terms GP is 11 , the sum of squares is 341 and sum of cubes is 3641.

0 votes
55 views

What is this geometric sequence?
The sum of first few terms geometric sequence is 11, the sum of squares is 341 and sum of cubes is 3641.

enter image description here

posted May 2 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

0 votes

1,-2,4,-8,16 and 16,-8,4,-2,1


a=first term, q=common ratio, n=number of terms.
Q=qn.
q=1 is impossible, as in that case an=11, a2n=341, and hence a=31, n=11/31, which contradicts to the condition a3n=3641
Therefore, the following relationships are true:
(1)-> a{Q-1 / q-1}=11
(2)-> a^2{Q^2-1 / q^2-1}=341
(3)-> a^3{Q^3-1 /r q^3-1}=3641
Divide (2) and (3) by (1).
Then a{Q+1 / q+1}=31 a^2{Q^2+Q+1 / q^2+q+-1}=331.
Hence a(Q-1)=11(q-1) (Q+1)=31(q+1) thus, a=10q+21 and Q={21q+10 / 10q+21}
Substitute the result into the equality a2(Q2+Q+1)=331(q2+q+1).
possible values of q : the roots of the equation 2q2+5q+2=0: q=-2 and q=-1/2.
Hence either a=1, Q=-32, n=5, or a=16, Q=-1/32, n=5.
Thus the solutions of the problem are the following two sequences: 1,-2,4,-8,16 and 16,-8,4,-2,1

answer May 2 by Hanifa Mammadov



Similar Puzzles
0 votes

The sum of the first three terms of a geometric progression is 8. The sum of the first six terms of the same geometric progression is 12.

Find the common ratio of this geometric progression?

0 votes

First and last term of a geometric progression are 3 and 96. If the sum of all these terms is 189, then find the number of terms in this progression.

0 votes

An arithmetic sequence formed of 11 terms, and the sum of all its terms equals to 220. Find the middle term in that sequence.

Contact Us
+91 9880187415
sales@queryhome.net
support@queryhome.net
#280, 3rd floor, 5th Main
6th Sector, HSR Layout
Bangalore-560102
Karnataka INDIA.
QUERY HOME
...