Question

The second term of a geometric sequence is 2 and the last term is 8. If the common ratio is square root of 2 , how many geometric means are there between the first term and the last term?

Answer 1

Answer:

there are 4 geometric means between 1st (✓2) and last term (8)

Step-by-step explanation:

2nd term = ar = a×✓2= 2

$a = \frac{2}{ \sqrt{2} } = \frac{ \sqrt{2} \times \sqrt{2} }{ \sqrt{2} } = \sqrt{2} \\ since \: \sqrt{2} \times \sqrt{2} = \sqrt{4} = 2$

the terms are

$\sqrt{2} \: \: \: \: 2 \: \: \: \: 2 \sqrt{2} \: \: \: \: 4 \: \: \: \: 4 \sqrt{2} \: \: \: \: 8$

there are 4 geometric means between 1st (✓2) and last term (8)