Question

What is the next term of the geometric sequence: `\frac { 4} { 9} ,- \frac { 4} { 3} ,4`?

Answer 1

`T_4 = -12`

Explanation:

To find the next term in a GP, (Geometric Progression/sequence) you have to multiply by the common ratio, `r`.

To find the value of`r`, divide one term by the preceding term:

`r = T_n/T_(n-1)` In this case, `r= T_3/T_2`

`r = 4 div (-4/3)`

`r = 4 xx-3/4 = -3`

Let's check by multiplying: `" "T_1 xx -3`

`4/9 xx -3 = -4/3`

So, `T_4 = 4 xx-3 = -12`

You will notice that ir `r` is negative, then then signs of the terms in the sequence alternate, positive, negative, positive, negative, etc.