For a natural number n, let a n =19 n -12 n . Then, the value of (31 α9-α10/57 α8) is

Question

For a natural number n, let a n =19 n -12 n . Then, the value of (31 α9-α10/57 α8) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

a n =19 n -12 n (31 α9-α10/57 α8)=(31(199-129)-(1910-1210)/57 α8) =(199(31-19)-129(31-12)/57 α8) =(199 ⋅ 12-1219 ⋅ 19/57 α8) =(12 ⋅ 19(198-128)/57 α8)=4

Q. For a natural number n, let an​=19n−12n. Then, the value of 57α8​31α9​−α10​​ is

an​=19n−12n 57α8​31α9​−α10​​=57α8​31(199−129)−(1910−1210)​ =57α8​199(31−19)−129(31−12)​ =57α8​199⋅12−1219⋅19​ =57α8​12⋅19(198−128)​=4

Q. For a natural number $n$ , let $a_{n} = 1 9^{n} - 1 2^{n}$ . Then, the value of $\frac{31 α _{9} - α _{10}}{57 α _{8}}$ is