cookiez69
What a stupid name, Nat.
- Joined
- Sep 16, 2012
- Messages
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- HSC
- 2014
Find a and b if a,b,1 forms a GP, and b,a,10 forms an AP.
Answer is...
GP:
a= 25/4
b= 5/2
AP:
a=4
b=-2
Also
a) Show that if the first, second and fourth terms of an AP form a geometric sequence, then either the sequence is a constant sequence, or the terms are the positive integer multiples of the first term.
b) Show that if the first, second and fifth terms of an AP form a geometric sequence, then either the sequence is a constant sequence, or the terms are the odd positive integer multiples of the first term.
c) Find the common ratio of the GP in which the first, third and fourth terms form an arithmetic sequence. [Hint: r^3 - 2r^2 + 1 = (r-1)(r^2 - r - 1)
d) Find the GP in which each term is one more than the sum of all previous terms.
Sorry for all the questions, but i'm stuck :\
Answer is...
GP:
a= 25/4
b= 5/2
AP:
a=4
b=-2
Also
a) Show that if the first, second and fourth terms of an AP form a geometric sequence, then either the sequence is a constant sequence, or the terms are the positive integer multiples of the first term.
b) Show that if the first, second and fifth terms of an AP form a geometric sequence, then either the sequence is a constant sequence, or the terms are the odd positive integer multiples of the first term.
c) Find the common ratio of the GP in which the first, third and fourth terms form an arithmetic sequence. [Hint: r^3 - 2r^2 + 1 = (r-1)(r^2 - r - 1)
d) Find the GP in which each term is one more than the sum of all previous terms.
Sorry for all the questions, but i'm stuck :\
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