Question

Sequences: If tn = 4n−1, find t1, t2, t3 and tn+1 . Express tn+1−tn in its simplest form.

Answer 1

t₁ = 3

t₂ = 7

t₃ = 11

`t_((n+1)) = 4 n + 3\\t_((n+1))-t_(n) =4\\`

Explanation:

Given:

`t_(n) = 4n - 1`

To Find:

t₁ = ?

t₂ = ?

t₃ = ?

`t_((n+1)) = ?\\t_((n+1))-t_(n) =?\\`

Solution:

Put n = 1 in the given equation we get

t₁ = 4×1 - 1 = 3

Put n = 2

t₂ = 4×2 - 1 = 7

Put n = 3

t₃ = 4×3 - 1 = 11

Put n = n + 1

`t_((n+1)) = 4(n+ 1) -1\\t_((n+1)) = 4n+4 -1 = 4n+3\\`

Now we want

`t_((n+1))-t_(n) = (4n + 3) - (4n-1)\\t_((n+1))-t_(n) = (4n + 3 - 4n+1)\\t_((n+1))-t_(n) = 4`