Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime and arithmetic sequence.
Find the smallest prime that is the fifth term of an increasing arithmetic sequence all four preceeding terms also being prime.
Smallest prime
Arithmetic Sequence
Algebra
But try the problem first...
Answer: is 29.
AIME I, 1999, Question 1
Elementary Number Theory by David Burton
First hint
Let the sequence be p, p+a, p+2a, p+3a, p+4a where p is prime and a is positive integer here p cannot be multiple of 2 or 3 or 4
Second Hint
then smallest p=5 taking a=6 we get a sequence of prime numbers
Final Step
5,11,17,23,29 then fifth term =29.
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