Question

Urgently need help!

S is a geometric sequence.

(a) Given that (√x-1), 1 and (√x + 1) are the first three terms of S, find the value of x.
You must show your work. (3 marks)

(b) Show that the fifth term of S is 7+5√2. (2 marks)

Answer 1

a)
`x=2`

b) see below

a) Since the first three terms are
`√(x)-1}`, 1 and
`√(x)+1}`, the middle term, 1, must be the geometric mean of the other two. Hence

`1^2=(√(x) -1)(√(x) +1)\implies`

`1=x-1\implies x=2`

b)

The common ratio is then
`√(2)+1`, and the first term is
`√(2) -1`.

Thus, the fifth term is

`(√(2) -1)*(√(2) +1)^4=(√(2) +1)^3`

`=(√(2) )3+3(√(2) )2+3(√(2) )+1`

`=2√(2) +6+3√(2) +1`

`=7+5√(2)`