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Seb Caster

What is this geometric sequence?

The sum of the first few terms in a geometric progression is 11, the sum of their squares is 341, and sum of their cubes is 3641. Find the terms of the sequence.

Posted in Math, asked by Seb Caster, 6 years ago. 2042 hits.

3

Let a=first term of the sequence, 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: a{Q-1 / q-1}=11 , a^2{Q^2-1 / q^2-1}=341 , a^3{Q^3-1 /r q^3-1}=3641. Divide the second and third equalities by the first one. 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 (from ane0) Q={21q+10 / 10q+21} Substitute the result into the equality a2(Q2+Q+1)=331(q2+q+1) above. 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.
Mariji Constante
Mariji Constante - 6 years ago
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0

In mathematics a geometric progression also known as a geometric sequence. It is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, 162.......

OR

A geometric sequence is one in which the same number is multiplied or divided by each element to get the next element in the sequence. 2, 4, 8, 16, ... is a geometric sequence.

 

Furqan Ali
Furqan Ali - 6 years ago
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-1

The terms of the series are: 1, -2, 4, -8, 16 or 16, -8, 4, -2, 1.
You have to set up three equations for the given three conditions and have to solve them. The procedure is time consuming and lengthy so instead of typing that all here I would like you to visit the URL given below in the reference, it explains the entire solution. Hope it clears. 

Hassan Shahbaz
Hassan Shahbaz - 6 years ago
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