Question

If a₁ = 2 and an = an-1 +5 then find the value of a5. for recursive sequence

Answer 1

`a_(5) = 22`.

Explanation:

In this recursive sequence, the value of the first term
`a_(1) = 2` is stated explicitly. The value of every other term of this sequence is given as an expression of the previous term.

For example, the value of the term
`a_(2)` (
`n = 2`) is given in terms of the value of
`a_(1)`:

`\begin{aligned}a_(2) &= a_((2 - 1)) + 5 \\ &= a_(1) + 5\end{aligned}`.

Likewise, the value of
`a_(3)` (
`n = 3`) would be:

`\begin{aligned}a_(3) &= a_((3 - 1)) + 5 \\ &= a_(2) + 5 \\ &= (a_((2-1))+5) + 5 \\ &= (a_(1) + 5) + 5 \\ &= a_(1) + 2 * 5 \\ &= a_(1) + (3 - 1) * 5\end{aligned}`.

In general, the value of
`a_(n)` (for integer
`n \ge 1`) would be:

`\begin{aligned} a_(n) &= a_(1) + (n - 1) * 5 \\ &= 2 + (n - 1) * 5\end{aligned}`.

Therefore, the value of
`a_(5)` (
`n = 5`) would be:

`\begin{aligned}a_(5) &= a_(1) + (5 - 1) * 5 \\ &= 2 + (5 - 1) * 5 \\ &= 22\end{aligned}`.