First, you have to see the behavior of the series: it has a negative number, then a positive number with a 5 addd (7+5=12), and this is repeated with the others values. Each termn has a 5 added. In this case, as there is negatives values alternated, the serie will have the termn (-1)^n. Then, we have:
a(n)=(-1)^n[ a + (n-1)d ]
a(n)=(-1)^n[ (7) + (n-1)(5) ]
a(n)=(-1)^n( 5n + 2 )
A possible expression for the serie –7 + 12 –17 +22 –27, is:
∑5n=(−1)^n(2+5n)
