Try this beautiful problem from Algebra: Arithmetic sequence from AMC 10A, 2015, Problem.
How many terms are in the arithmetic sequence $13$, $16$, $19$, $\dotsc$, $70$, $73$?
Algebra
Arithmetic sequence
Answer: \(21\)
AMC-10A (2015) Problem 7
Pre College Mathematics
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 ..........
$a+(n-1) d \Longrightarrow 13+(n-1) 3=73$
\(\Rightarrow n=21\)
The number of terms=\(21\)
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