Question

How do you find the first term in a geometric sequence?

Answer 1

I usually do that by the definition:

\[\Large a_n=a_1q^{n-1} \] But Maybe you have an example.

Answer 2

It's to do with a rather difficult problem:
"The roots of 2x^3+21x^2+mx+q=0 are in geometric progression with a ratio of 2. Find the values of m and q and the roots."

I thought I would start by finding the roots in geometric progression, but all the formulas I find require the first term, which i don't know.

Answer 3

can someone please help me? @azolotor ?

Answer 4

question not clear to me fully

Answer 5

i have to find the roots of the equation above. the roots are in geometric progression with a ratio of two. i dont know where to start without the first term of teh geometric sequence, so i was wondering if anyone knew how to find the first term in a geometric series/sequence?

Answer 6

u see the roots are in geometric progression, so u have to find the roots first and u will see there will come m and q in the roots some where which after applying the progression rules will become known.

Answer 7

how would you find the roots if you don't know m and q?

Answer 8

i think if one of the roots(smaller one) is "r" then the other two will b 2r and 4r as is given.
if u put these values one by one in the equation u get three equations in three unknowns solve them to get the value of r

Answer 9

this way u get r p m as these are the three unknowns and u have three equations

Answer 10

i dont really understnad what you mean by put them in the equations and solve for r

Answer 11

the roots are in GP

let r be one of the roots , the smaller one

then the next two will be 2r and 4r as the ratio is 2

since these are the roots, will satisfy the given equation,

put them one by one in the original equation u will get three equation with three unknowns

solve them to get the values of r p m

Answer 12

ok ill try that

Answer 13

wait how do you solve an equation with three unknown variables?

Answer 14

three equations three unknowns is a system of three equations which u get by putting r 2r and 4r respectively in the equation and then solve them

Answer 15

oh k

Answer 16

would this be how to set it up?