Answer:
Arithmetic sequence states that a sequence of numbers such that the difference between the consecutive terms is constant.
it is given by: \(a_n = a+(n-1)d\) where a is the first term , n is the number of term and d is the common difference.
Given the series: \(49 + 54 + 59+ ......\)
here, Common difference(d) = 5
First term(a) = 49
by definition we have;
For nth term
\(a_n = a+(n-1)d\)
\(a_n = 49+(n-1)5\)
\(a_n =49+5n -5\) = 5n + 44
To write the series using summation notation for 14 terms
Summation symbol \('\sum'\)
The series for 14th terms is given by;
\(\sum_{n=1}^{14}(5n +44)\)
