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Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime and arithmetic sequence.

## Smallest prime Problem – AIME I, 1999

Find the smallest prime that is the fifth term of an increasing arithmetic sequence all four preceeding terms also being prime.

- is 107
- is 29
- is 840
- cannot be determined from the given information

**Key Concepts**

Smallest prime

Arithmetic Sequence

Algebra

## Check the Answer

But try the problem first…

Answer: is 29.

Source

Suggested Reading

AIME I, 1999, Question 1

Elementary Number Theory by David Burton

## Try with Hints

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.

## Other useful links

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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