Question

Which is a possible expression for the series –7 + 12 –17 +22 –27

Answer 1

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)