given s n sum of first n natural no s then z n 2 s n 41 least value of

for 41 z(n) = 1681
which has factors 1,41 and 1681 so
answer is (d)
8 years agoHelpfull: Yes(5) No(6)
Z(n) always prime
7 years agoHelpfull: Yes(5) No(5)
6 is the ans
8 years agoHelpfull: Yes(3) No(0)
ans-(d), z(41)=41*43 after solving since 41 is a prime no. z(n) is divisible it means z(n) is not prime
7 years agoHelpfull: Yes(1) No(0)
d) 41
as it gives 1763 and it is divisible by 43
7 years agoHelpfull: Yes(1) No(0)
s(n) = sum of n natural numbers = n(n+1)/2 because n numbers of natural numbers are 1+2+3+4+5+...+n which are in a.p. with d=1 a= 1 and LAst Term(L) = n so by formula s(n ) = n/2*(a+L) s(n) = n(n+1)/2 putting this in equation not going to show calculation z(n) = n(n+1) +41 some times after some steps u need to hit and try in elitmus cause that is the faster way so for n= 41 we can use reverse substitution and by that i mean instead of 41 put n z(n)= n(n+1) + n z(n) = n(n+2) by this we can see z(n) is not prime as it is a multiplication of two numbers a prime number can only have factors 1 for 41 z(n) = 1681 which has factors 1,41 and 1681 so answer is (d)
6 years agoHelpfull: Yes(1) No(0)
in question it's clear about least value.....
so we will take first =6(option b)
so s(n)=21
given equation is z(n)=2*s(n)+41
=2*21+41
=83(prime number)
ans b is correct
6 years agoHelpfull: Yes(1) No(0)
check options n=6 s(n)=21 z(n)=83 prime n=7 s(n)=28 and z(n)=97 prime and n=41 z(n)=1681 which is not an prime
8 years agoHelpfull: Yes(0) No(3)

given s(n) sum of first n natural no's then z(n)=2 s(n)+41 least value of n that gives z(n) is not prime?
a)z(n) always prime
b)6
c)7
d)41