Hi! A new concept is being introduced and I'd like to figure out some of these examples with answers.

First one

First term  = 2(1)  = 2

Fifth term  = 2(5)  = 10

Sum of series  =

[ first term + last term ] *  number of terms  /  2    =

[ 2 + 10 ] * [ 5] / 2  =

12 * 5 / 2  =

60 / 2  =

30

Second one...not arithmetic or geometric......probably easiest to just list the terms

First term  ( 2 * 1)^2  =  4

Second term  = (2 * 2)^2  =  16

Thirs term = (2 * 3)^2  = 36

Fourth term  (2 * 4)^2 = 64

Sum  = 120

Last one

First term  =  -2(3) + 5  =  -1

Last term = -2(6) + 5 =  -7

Sum

[ first term + last term ] * number of terms  / 2  =

[ -1 + -7 ] *  4  / 2  =

-8 * 4  / 2  =

-16