A number theory problem by Varun Bansal

Um, why can't the answer be, say, 1175?

If $f(x) = \frac{1}{3}(2x^4 - 24x^3 + 100x^2 - 402x + 105) \implies f(1)=195, f(2)=383,f(3)=575,f(4)=763,f(5)=955,f(6)=1175$

Or for that matter, any of an infinite number of other answers, depending on which polynomial you pick.

as the number pattern shows: 1st digit from left side is odd and in ascending order=11 10th place is descending order=4 ones place is aternate of 5 and 3 so next number =3

Here is the pattern:

aₙ=aₙ₋₁+188((n-1) mod 2)+192(n mod 2)

if a₁=195, a₂=383, ...

a₆=955+188 (5mod2)+192 (6mod2)=1143

There is a pattern in in even and odd numbers. 1st digit from left is increasing by 4 (from n-2) and middle digit is decreasing by 2(from n-2) and last digit is constant (same as n-2). Hence 1143 will be the solution.