Geometric sequence

[Ashiya]

If m-1, m+3 and m+12 are consecutive terms in a geometric sequence, determine the values of the three terms for all such sequences??

 

[Deleted member 4993]

If m-1, m+3 and m+12 are consecutive terms in a geometric sequence, determine the values of the three terms for all such sequences??

Consecutive terms in a geometric series looks like ar[sup:3kuu13v4]n[/sup:3kuu13v4]. ar[sup:3kuu13v4]n+1[/sup:3kuu13v4] and ar[sup:3kuu13v4]n+2[/sup:3kuu13v4]

then

\(\displaystyle r \, = \frac{ar^{n+1}}{ar^n} \, = \, \frac{{m+3}}{m-1} .............................(1)\)

and

\(\displaystyle r \, = \frac{ar^{n+2}}{ar^{n+1}} \, = \, \frac{{m+12}}{m+3} .............................(2)\)

Equating (1) and (2)

\(\displaystyle (m+3)^2 \, = \, (m-1)\cdot (m+12)\)

solve the equation above to find 'm'.

 

[Aladdin]

Let a=m-1 , b=m+3 ,c=m+12.
Since they are 3 concequtive numbers,and its a Geometric sequence:So,
b/a=c/b ---------- Solve for m and then substitute .

Right Mr Khan,?

 

[stapel]

Let a=m-1 , b=m+3 ,c=m+12.
Since they are 3 concequtive numbers,and its a Geometric sequence:So,
b/a=c/b ---------- Solve for m and then substitute .

Right Mr Khan,?

Yes, you have correctly restated what the tutor had posted.

 

[Aladdin]

Re:

Let a=m-1 , b=m+3 ,c=m+12.
Since they are 3 concequtive numbers,and its a Geometric sequence:So,
b/a=c/b ---------- Solve for m and then substitute .

Right Mr Khan,?

Yes, you have correctly restated what the tutor had posted.

That means Correct :wink: .