Given the 2 sequences :
1.Calculate the common difference :
• F(n+1 ) = F(n) -8 ,
f(1) = 9 for n>=1
f(2) = F(1) -8 = 1
f(3) = f(2) -8 = -7
f(4) =f(3) -8 = -15
• so the common difference = -15-(-7) = -8
or d =-7 -(1) = -8, so d = -8
2. Calculating the 38th term would be :
f(38) = f(1) +37d
= f(1) + 37 *(-8)
= 9 + -296
= -287
• This means that the ,38th term = -287,