Try this beautiful problem from Algebra: Arithmetic sequence from AMC 10A, 2015, Problem.

Arithmetic sequence – AMC-10A, 2015- Problem 7


How many terms are in the arithmetic sequence $13$, $16$, $19$, $\dotsc$, $70$, $73$?

  • \(20\)
  • \(21\)
  • \(24\)
  • \(60\)
  • \(61\)

Key Concepts


Algebra

Arithmetic sequence

Check the Answer


But try the problem first…

Answer: \(21\)

Source
Suggested Reading

AMC-10A (2015) Problem 7

Pre College Mathematics

Try with Hints


First hint

The given terms are $13$, $16$, $19$, $\dotsc$, $70$, $73$. We have to find out the numbers of terms…..

If you look very carefully then the distance between two digits is \(3\).Therefore this is an Arithmetic Progression where the first term is \(13\) and common difference is \(3\)

Can you now finish the problem ……….

Second Hint

$a+(n-1) d \Longrightarrow 13+(n-1) 3=73$

\(\Rightarrow n=21\)

The number of terms=\(21\)

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