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#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")