Question

Help? Fan and medal will be given.

Find the missing terms of the following geometric sequence. (The geometric mean of the first and fifth terms is the third term. Some terms might be negative.)

1.5, ___, ___, ___, 1215,...

a2 =
a3 =
a4 =

Thank you in advance!

Answer 1

How would I find the three terms?

Answer 2

Geometric sequence always follows a pattern,

\(\color{#000000}{ \displaystyle a_2=r\times a_1 }\)
\(\color{#000000}{ \displaystyle a_3=r^2\times a_1 }\)
\(\color{#000000}{ \displaystyle a_4=r^3\times a_1 }\)
\(\color{#000000}{ \displaystyle a_5=r^4\times a_1 }\)
......
\(\color{#000000}{ \displaystyle a_n=r^{n-1} \times a_1 }\)

Correct ?

Answer 3

in other words, you always multiply times a common ratio r in there.

Answer 4

Your first term is 1.5, and your fifth term is 1215.
\(\color{#000000}{ \displaystyle a_5=r^{4} \times a_1 }\)
\(\color{#000000}{ \displaystyle 1.5=r^{4} \times 1215 }\)

Answer 5

Solve for the comon ratio (and note that common ratio r can be positive or negative, so the 2nd and 4th term can be \(\pm\))

Answer 6

Okay, thank you very much :) I'll use these to solve and tell you if I need help.

Answer 7

sounds like a good plan.
you welcome.