Question

The

term-to-term rule for a sequence is given as u_n+1=u_n+2

a) Explain in words what this means.

b)Given that u, = -4, list the first five terms of the sequence.

Answer 1

- 8, - 6, - 4, - 2, 0

Explanation:

the term- to- term rule

`u_(n+1)` =
`u_(n)` + 2

means that to find a term in the sequence you add 2 to the previous term.

given u₃ = - 4 , then

u₄ = u₃ + 2 = - 4 + 2 = - 2

u₅ = u₄ + 2 = - 2 + 2 = 0

to find the first 2 terms, rearrange the rule as

`u_(n+1)` =
`u_(n)` + 2 ( subtract 2 from both sides )

`u_(n+1)` - 2 =
`u_(n)` , that is

`u_(n)` =
`u_(n+1)` - 2

this allows for a term to be found by subtracting 2 from the next term, so

a₂ = a₃ - 2 = - 4 - 2 = - 6

a₁ = a₂ - 2 = - 6 - 2 = - 8

the first 5 terms are then : - 8, - 6, - 4, - 2, 0