to work out the sum of the nth term yo ucan use the common equation such that
n/2(2a+((n-1)d))
such as
n= the number of terms
a=the first term
d=the comon difference between each term
However when there is no nth term but the first and last term are know you can use a more difficult equation derived from two seperate one:
1--nth term if not given
(L-a/d)+1 L is the last term A is the first and d is common differenc
2--sum of terms with last term known- n/2(a+L)
Number 2 is derived from the sn=n/2(2a+(n-1)d) which expands to give
n/2(a+a+(n-1)d) which when incorporating nth term equation of a+(n-1)d give n/2(a+l)
1 and 2 combine to give a formula such sa you can work out the sum of the term without knowing the nth term but knowing the last it is given as
((l-a)/d)=1)/2 times (a+l)
in steps,,
l-a
ans divided by d
ans plus 1
ans divided by 2
ans times by l+a
all this is useing the as level arithmetic sequences equartions.