Question

Describe when it is easier to use the formula Sn= n/2(a+tn) and when the formula Sn= n/2[[2a+ (n-1) d] is a better choice.

Answer 1

$$S_n=\dfrac{n}{2}(a_1+a_n)$$

We use this formula for the nth partial sum if the first term $a_1,$ the nth term $a_n,$ and the number of terms $n$ are given.

$$S_n=\dfrac{n}{2}(2a_1+(n-1)d)$$

We use this formula for the nth partial sum if the first term $a_1,$ the difference $d,$ and the number of terms $n$ are given.