The number of terms n is 7.
Explanation:
Given that:
First term a=21
nth term [tex]a_{n}[/tex]=39
Sum up to n terms [tex]S_{n}[/tex]=210
To Find:
The number of terms n in the arithmetic progression.
Formula to be used:
Sum up to n terms Sn is given by the expression
[tex]S_{n} =\frac{n}{2} (a+a_{n} )[/tex]
Solution:
[tex]S_{n} =\frac{n}{2} (a+a_{n} )\\\\210=\frac{n}{2}(21+39)\\\\210=\frac{n}{2}(60)=30n\\\\n=210/30=7[/tex]
Number of terms n in the given series is n=7
