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

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

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

Algebra

Arithmetic sequence

But try the problem first...

Answer: \(21\)

Source

Suggested Reading

AMC-10A (2015) Problem 7

Pre College Mathematics

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=\(21\)

- https://www.cheenta.com/surface-area-of-cube-amc-10a-2007-problem-21/
- https://www.youtube.com/watch?v=VLyrlx2DWdA&t=20s

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