Question

If r = -\sqrt{2}, and a5 = \sqrt{2}, what is the first term of the sequence?

Select the letter of the correct answer.

A. \sqrt{2}

B. 8\sqrt{2}

C. 4\sqrt{2}

D. 2\sqrt{2}

Answer 1

Answer: C

Explanation:

Let x represent the first term (a₁)

a₁ = x

a₂ = x(-√2) = -x√2

a₃ = -x√2(-√2) = 2x

a₄ = 2x(-√2) = -2x√2

a₅ = -2x√2(-√2) = 4x

Since it is given the a₅ = √2, then we can solve: 4x =√2

Divide both sides by 4 to get: x =
`(√(2))/(4)`

this can also be written as:
`(1)/(4)√(2)`