Recursive sequence

Question

If a₁ = 7 and a_n = a_n-1-4 then find the value of a₆

Answer 1

common difference = d = -4

an= a1 + (n-1)d is the formula for the nth term of an arithmetic sequence with common difference = d

for n=6

a6 = 7 +(6-1)(-4) = 7-20 = -13

a6 = -13

or do it another way with the recursive formula, but that will be time consuming if n is very large

a1 = 7

a2 =7-4= 3

a3 =3-4 =-1

a4 = -1-4 = -5

a5 = -5-4 = -9

a6 = -9-4 = -13

if you get the same answer doing it two different ways, you feel very confident there is no mistake