Sum of n terms of Arithmetic progression (AP) is

Sum = (n/2)*{2a + (n-1)*d}

where n = Number of terms in AP

          a = First term of AP

          d = Common difference of AP

1. Given Arithmetic Series is:

2,7,10,.....,to 10 terms

Here a =2, n = 10, d = 7-2 = 5

sum = (10/2)*{2*2 + (10-1)*5}

       = 5*(4 + 9*5)

       = 5*(4 + 45)

       = 5*49

       = 245

=> Sum = 245

2.  Given Arithmetic Series is:

-37,-33,-29,.....,to 12 terms

Here a =-37, n = 12, d = -33-(-37) = -33 + 37 = 4

sum = (12/2)*{2*(-37) + (12-1)*4}

       = 6*(-74 + 11*4)

       = 6*(-74 + 44)

       = 6*(-30)

       = - 180

=> Sum = - 180

3. Given Arithmetic Series is:

0.6,1.7,2.8,.....,to 100 terms

Here a =0.6, n = 100, d = 1.7 - 0.6 = 1.1

sum = (100/2)*{2*0.6 + (100-1)*1.1}

       = 50*(1.2 + 99*1.1)

       = 50*(1.2 + 108.9)

       = 50*110.1

       = 5505.0

=> Sum = 5505.0

4. Given Arithmetic Series is:

1/15,1/12,1/10,.....,to 11 terms

Here a =1/15, n = 11, d = 1/12 - 1/15 = 1/60

sum = (11/2)*{2*(1/15) + (11-1)*(1/60)}

       = (11/2)*(2/15 + 10/60)

       = (11/2)*(18/60)

       = (11*18)/(2*60)

       = (11*3)/(2*10)        (when 18 and 60 is divided by 6)

       = 33/20

=> Sum = 33/20