Question

If $a_1=a_2=2,a_n=a_{n-1}-1(n>2),$then $a_5$is

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is B

$-1$

Find the value of ${\mathit{a}}_{\mathbf{5}}$:

Given that $a_1=a_2=2,a_n=a_{n-1}-1(n>2),$

$a_n=a_{n-1}–1........\left(i\right)$

Put $n=3$ in the equation (i). we get

$$\begin{gathered} a_3=a_{(3-1)}–1 \\ {a}_3=a_2–1 \\ {a}_3=2-1=1 \end{gathered}$$

Put $n=4$ in the equation (i). we get

$$\begin{gathered} a_4=a_{(4-1)}–1 \\ {a}_4=a_3–1 \\ {a}_4=1–1=0 \end{gathered}$$

Put $n=5$ in the equation (i). we get

$$\begin{gathered} a_5=a_{(5-1)}–1 \\ {a}_5=a_4–1 \\ {a}_5=0–1=-1 \end{gathered}$$

Hence, the correct option is ( B).