In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41

Question

(a) In the sequence A, A1 = 43, A2 = 47,..............., Ak = k^2 + k + 41. 
 Is every term in sequence A a prime number?
 
 (1) There are fewer than 999 terms in sequence A.
 (2) There are more than 99 terms in sequence A.

toddmartin · Answer

If I undestand the problem right then Ak=2*k+k+41. So A2=2*2+2+41=4+2+41=6+41=47.

 Wouldn't A5=2*5+5+41, so A5=10+5+41=15+41=56. 

 Since 56 is divisible by 2 it is not prime and I don't need the statements to tell me that every number in the set is not prime. Am I reading the problem wrong?

FN · Answer

I believe the answer is D, that is if it K^2. all numbers are prime!

I checked for the first 10 numbers, and then figure that the sequence repeats itself so in an infintite chain there are infinite prime numbers, either statement can be used!

MA · Answer

I have edited the problem. k2 = k square

vprabhala · Answer

can somebody elaborate how to approach such problems. i have difficulty in doing these..

MA · Answer

vprabhala,

this my understanding.

from i, number of terms can 1,2,3,4,5,6, ............... 999.
if the number of terms in the series is 1, then 
A1= 1+1+41= 43. the answer is yes.
if the number of terms in the series is 41, then 
A41= 41^2+41+41=41(43). then answer is no because A41 is devided by 41 and 43.

from ii, the number of terms in series is more than 99 means, the series is A1, A2, ....., A41, ........, A82, .........An
the terms A41 and A82 are at least not prime. therefore, the answer is B.

jinino · Answer

From i), there are fewer than 999 items in the series, and since A40, A41 are not prime, and other numbers can be prime, so from i) alone we can say 'no' to the question asked.

From ii), there are more than 99 items in series, and again A40, A41, A82 are not prime, and other numbers can be prime, so again from ii) we can say 'no' to the question asked.

Can you clarify your answer, MA? Thanks.

MA · Answer

jinino,
statement (i) is insufficient to answer the question because if the term in the series is only 1, then every term in the series is prime, but if the terms in the series are 41 or 82, then every term in the series is not prime.

statement (ii) is sufficient to answer the question because there are more than 99 terms in the series means there are at least 100 terms in the series. this series includes terms 41 and 82 and these terms in the series are not prime.

if we read the question stem carefully, it is clearly mentioned that every term in the series. this is the clue to the solution.

jinino · Answer

I got it now, MA. :thanks

In the sequence A, A1 = 43, A2 = 47,...,Ak = k^2 + k + 41

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