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

Let P(n)=11n+2+122n+1, then the least value of the following which P(n) is divisible by is

A
19
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
7
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
133
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
none of these
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

The correct option is B 7Given that P(n)=11n+2+122n+1Put n=1 to obtain P(1)=111+2+122+1=3059=7(437)Therefore, P(1) is divisible by 7Assume that for n=k, P(k)=11k+2+122k+1 is divisible by 7Now, P(k+1)=11k+3+122k+3=11.11k+2+144.122k+1=11(11k+2+122k+1)+133⇒P(k+1)=11P(k)+7(79)SInce, P(k) is divisible by 7Therefore, P(k+1) is divisible by 7And from the principle of mathematical induction P(n) is divisible by 7 for all n∈NAns: B

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Extrema
MATHEMATICS
Watch in App
Join BYJU'S Learning Program