Find the sum of the following arithmetic series:
3 +7 +11 +15 +... +47.
The sum of this series is___

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 = where, n is the number of term, a is the first term and l is the last term.

nth term of a series = = 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 = (3+47) = 300

a

step-by-step explanation:

step-by-step explanation:

one day the were 5 ducks, and their king told them to multiply their kingdom. so each went their own seperate way and met 4 other ducks on their journey.

when the ducks returned to their kingdom, it was discovered that there were 5 groups of 5 ducks. when the kind counted the number of ducks in total (including the ones he sent out earlier) he counted 25.

therefore 5 times 5 is 25.

the end. : )