#GGearing
#02/10/2017
#Simple script to calculate the quadratic formula of a sequence of numbers and
#recognises when the sequence isn't quadratic

def findLinear(numbers):    ##find a & b of linear sequence
    output=[]
    a=numbers[1]-numbers[0]
    a1=numbers[2]-numbers[1]
    if a1==a:
        b=numbers[0]-a
        return (a,b)
    else:
        print("Sequence is not linear")
        
sequence=[]
first_difference=[]
second_difference=[]
for i in range(4):  #input
    term=str(i+1)
    inp=int(input("Enter term "+term+": "))
    sequence.append(inp)
    
for i in range(3):
    gradient=sequence[i+1]-sequence[i]
    first_difference.append(gradient)
for i in range(2):
    gradient=first_difference[i+1]-first_difference[i]
    second_difference.append(gradient)
    
if second_difference[0]==second_difference[1]:  #checks to see if consistent
    a=second_difference[0]/2
    subs_diff=[]
    for i in range(4):
        n=i+1
        num=a*(n*n)
        subs_diff.append((sequence[i])-num)
    b,c=findLinear(subs_diff)
    print("Nth term: "+str(a)+"n^2 + "+str(b)+"n + "+str(c)) #outputs nth term
else:
    print("Sequence is not quadratic")