Question

Find the 16th term of the geometric sequence 4, -16, 64, ...

Answer 1

`\bold{a_(16) =-4^(16)=-2^(32)=-4\,294\,967\,296}`

Explanation:

`a_1=4\\a_2=-16\\a_3=64\\\\(a_2)/(a_1)=(-16)/(4)=-4\\\\ (a_3)/(a_2)=(64)/(-16)=-4\\\\\\(a_2)/(a_1)=(a_3)/(a_2)=-4=r`

The formula:

`a_n=a_1\cdot q^(n-1)`

Therefore:

`a_(16) =4\cdot(-4)^(16-1)=4\cdot(-4)^(15)=-4^(16)=-2^(32)=-4\,294\,967\,296`