Question

If a1=7 and an = an-1-3 then find the value of a4

Answer 1

it is given

first term

a1 = 7

the equation of nth term is,

$a_n=a_{n-1}-3$

put n = 2

$\begin{gathered} a_2=a_{2-1}-3 \\ =a_1-3 \\ =7-3 \\ =4 \end{gathered}$

put n = 3

$\begin{gathered} a_3=a_{3-1}-3 \\ =a_2-3 \\ =4-3 \\ =1 \end{gathered}$

put n= 4

$\begin{gathered} a_4=a_{4-1}-3 \\ =a_3-3 \\ =1-3 \\ =-2 \end{gathered}$

thus, the answer is a4 = -2