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