Given series is

1.  7 + 14 + . . . + 84

First term a = 7

Common diference d = 14 - 7 = 7

Last term l = 84

Let number of terms is n.

Now l = a + (n-1)d

=> 84 = 7 + (n-1)7

=> 84 - 7 = (n-1)7

=> 7(n-1) = 77

=> n-1 = 77/7

=> n-1 = 11

=> n = 11+1

=> n = 12

Now sum S_n = (n/2)*(a + l)

                    = (12/2)*(7 + 84)

                    = 6 * 91

                    = 546

So sum = 546

2.  34 + 32 + . . . + 10

First term a = 43

Common diference d = 32 - 34 = - 2

Last term l = 10

Let number of terms is n.

Now l = a + (n-1)d

=> 10 = 34 + (n-1)*(- 2)

=> 10 - 34 = (n-1)(- 2)

=> -2 *(n-1) = -24

=> n-1 = 24/2

=> n-1 = 12

=> n = 12+1

=> n = 13

Now sum S_n = (n/2)*(a + l)

                    = (13/2)*(34 + 10)

                    = (13 * 44)/2

                    = 13*22

                    = 286

So sum is 286

3.  -5 + (-8) + . . . + (-230)

First term a = -5

Common diference d = -8 - (-5) = - 8 + 5 = -3

Last term l = -230

Let number of terms is n.

Now l = a + (n-1)d

=> -230 = -5 + (n-1)*(- 3)

=> -230 + 5 = (n-1)(- 3)

=> -3 *(n-1) = -225

=> n-1 = 225/3

=> n-1 = 75

=> n = 75+1

=> n = 76

Now sum S_n = (n/2)*(a + l)

                    = (76/2)*{-5 + (-230)}

                    = (76/2)*(-5 - 230)

                    = - 38*235

                    = - 8930

So sum is  - 8930