Question

The 2nd and 3rd terms in the following algebraic sequence are x and y. Write down algebraic expressions for the first, fourth and fifth terms.

Answer 1

see explanation

Explanation:

To obtain a term in the sequence add the previous 2 terms, that is

`a_(n)` =
`a_(n-1)` +
`a_(n-2)` ← in general terms

(a)

Given 1 4 5 9 14

Then the next 2 terms are 9 + 14 = 23 and 23 + 14 = 37

(b)

Given a₄ = 30 and a₅ = 49 , then

a₃ = 49 - 30 = 19

a₂ = 30 - 19 = 11

a₁ = 19 - 11 = 8

Sequence is 8 11 19 30 49 ....

(c)

Given a₂ = x and a₃ = y , then

a₁ = y - x

a₄ = a₃ + a₂ = y + x

a₅ = a₄ + a₃ = y + x + y = 2y + x