How many terms are there in the series 199,208,217,…,406?

The given series is an Arithmetic Progression (AP):
First term (a) = 199

Common difference (d) = 208−199=9

Last term (a
n
​
) = 406

The formula for the n-th term of an AP is:

a
n
​
=a+(n−1)d
Substitute the known values into the equation:

406=199+(n−1)×9
406−199=9(n−1)
207=9(n−1)
n−1=
9
207
​

n−1=23
n=24
Thus, there are 24 terms in the series.