Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Olympiad workbookIOQMFunctions

Let x₁ be a positive real number and for every integer n 1 let x_ n+1 =1+x₁ x₂ x_ n-1 x_n . If x₅=43 , what is the sum of digits of the largest prime factor of x₆ ?

Correct answer

13

Step-by-step solution

array ll x₅=1+x₁ x₂ x₃ x₄ & x₁ x₂ x₃ x₄=42 x₆=1+x₁ x₂ x₃ x₄ x₅ & =1+(42)(43)=1807=13 139 array largest prime factor =139 sum of digits =13

Practice Functions on Quantrex Academy →

More from Functions

Let n be a positive integer such that 1 n 1000 . Let M_n be the number of integers in the set X_n= 4 n+1 , 4 n+2 , ., 4 n+1000 . Let a= M_n: 1 n 1000 and b= M_n: 1 n 1000 . Find a-Positive integers x, y, z satisfy x y+z=160 . Compute the smallest possible value of x+y z .Consider the sequence of number [n+ 2 n + 1 2 ] for n 1 , where [x] denotes the greatest integer not exceeding x . If the missing integers in the sequence are n₁ < n₂ < n₃ < then fLet x₁ be a positive real number and for every integer n 1 let x_ n+1 =1+x₁ x₂ x_ n-1 x_n . If x₅=43 , what is the sum of digits of the largest prime factor of x₆ ?Let f: R R be a function satisfying the relation 4 f(3-x)+3 f(x)=x^2 for any real x . Find the value of f(27)-f(25) to the nearest integer. (Here R denotes the set of real numbers.Let f(x)= x 3 + 3 x 10 for all real x . Find the least natural number n such that f(n +x)=f(x) for all real x .Find the largest value of a^b such that the positive integers a, b>1 satisfy a^b b^a+a^b+b^a=5329 .The sum of [x] for all real numbers x satisfying the equation 16+15 x+15 x^2=[x]^3 is: Full Functions list All Olympiad workbook PYQs