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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

But try the problem first…

Answer: $21$

Source

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=$21$