What is the sequence of the n^"th" term equation f(n) = -3n +7 for n 1

The sequence of the given equation

         4 , 1, -2 , -5, ......

∴ The given sequence is in Arithmetic progression ( A.P)

Step-by-step explanation:

Step(i):-

Given term of thesequence

                  f (n) = - 3n + 7

Put n = 1

     first term  a₁ = f (1 ) = - 3 (1 ) + 7 = - 3 + 7 = 4

Put n = 2

     second term  a₂ = f(2) = - 3 ( 2) + 7 = -6 +7 =1

Put n =3

     Third term   a₃ = f(3) = -3(3) +7 = -9 + 7 = -2

Put n =4

   Fourth term  a₄ = f(4) = -3(4) +7 = -12 + 7 = -5

Step(ii):-

The sequence of the given equation

         4 , 1, -2 , -5, ......

first term a = 4 , d = 1 -4 = -3

The difference of two terms in this sequence is equal

∴ The given sequence is in Arithmetic progression ( A.P)

Final -

  The sequence of the given equation

         4 , 1, -2 , -5, ......

∴ The given sequence is in Arithmetic progression ( A.P)              

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.