The 4th term of a geometric sequence if the second term is 4 and the sixth term is 16

Question

Using an equation

Answer 1

The nth term of a geometric sequence = ar^(n – 1)

2nd term =4=ar^(2-1)=ar

ar=4    .........eq1

6th term=16=ar^(6-1)=ar^5

ar^5=16  ........eq2

eq2/eq1 gives

ar^5/ar=16/4

r^4=4

(r^2)^2=2^2

r^2=2

r=sqrt2

substituting in eq1 we get

a(sqrt2)=4

a=4/(sqrt2)=2sqrt2

4th term=ar^3=2sqrt2(sqrt2)^3=2(sqrt2)^4=2(4)=8