Question

7.5^(2n-1)+2^(3n-1) is divisible by 17​

Answer 1

Step-by-step explanation:

Given 7.5^(2n-1)+2^(3n+1) is divisible by 17

• Now let  
•    P(n) = 7 x 5^2n – 1 + 2^3n + 1
•    So P(1) = 7 x 5^2(1) – 1 + 2^3(1) + 1
•                 = 7 x 5^1 + 2^4
•                 = 35 + 16
•    So P(1) = 51
•   Now P(2) = 7 x 5^2(2) – 1 + 2^3(2) + 1
•                   = 7 x 5^3 + 2^7
•                    = 7 x 125 + 128
•                     = 875 + 128
•       So P(2) = 1003
• Now we need to find hcf of P(1) and P(2)
• So hcf of 51 and 1003
• So factors of  
•      51 = 3 x 17
•    1003 = 17 x 59
• So 17 will be the hcf
• Therefore the given expression is divisible by 17

Reference link will be

https://brainly.in/question/7854002

Answer 2

Answer:

by method of induction it is proved