1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Let P(n)=n(n2+20) is divisible by 48, then for which of the following P(n) is true

A
nN
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
n odd natural number
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
n even natural numbers
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C ∀n∈ even natural numbersP(n)=n(n2+20)When n is even, then n(n2+20)=2k(2k2+20)=2k×4×(k2+5) divisible by 8 for sure.Let n=8P(8)=8(82+20)=8(84)=672 is divisible by 48.Let n=17P(17)=17(172+20)=17(309)=5253 is not divisible by 48.Let n=26P(26)=26(262+20)=26(696)=18096 is divisible by 48.Let n=9P(9)=9(92+20)=9(101)=909 is not divisible by 48.So, we can conclude that for all even n, it is divisible by 48.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Remainder Theorem
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program