Question

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

Answer 1

Answer:

$a_{5} = 22$.

Step-by-step 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:

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

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

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

Therefore, the value of $a_{5}$ ($n = 5$) would be:

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