Question

What is the equation for the nth term of geometric sequence 32,48,72

Answer 1

`\bold{a_n =32\left(\frac32\right)^(n-1)}`

Explanation:

`a_1=32\\a_2=48\\a_3=72\\\\(a_2)/(a_1)=(48)/(32)=\frac32\\\\ (a_3)/(a_2)=(72)/(48)=\frac32\\\\\\(a_2)/(a_1)=(a_3)/(a_2)=\frac32=r`

Therefore the formula:

`a_n=a_1\cdot q^(n-1)\\\\a_n =32\left(\frac32\right)^(n-1)`