The sum of the given series is 300.
Step-by-step explanation:
Given,
The arithmetic series: 3+7+11+15+.....+47
To find the sum of the series.
Formula
Sum of the series = [tex]\frac{n}{2}(a+l)[/tex] where, n is the number of term, a is the first term and l is the last term.
nth term of a series = [tex]a_{n}[/tex] = a+(n-1)d where d is the common difference
Now,
Here, a=3
d = 7-3 = 11-7=15-11=4
Hence,
47 = 3+(n-1)4
or, 4(n-1) = 47-3
or, 4(n-1) = 44
or, n-1 = 11
or, n = 12
Now,
Sum = [tex]\frac{12}{2}[/tex] (3+47) = 300
