Given series is:

    1 - 3 + 5 - 7 + 9 - 11 + 13 - 15 + ........

= (1 + 5 + 9 + 13 + .......upto 60 term) - (3 + 7 + 11 + 15 + ........upto 60 terms)

Now, we find the sum of 60 terms in first series and find the sum of 60 terms in second

series, we get the find the sum of first 120 terms in the given series.

Now, 1 + 5 + 9 + 13 + .......upto 60 term

It forms an AP

Now, Sum of 1st series = (n/2) *{2a + (n - 1)d}

                                  = (60/2) * {2 * 1 + (60 - 1)4}

                                  = 30 * (2 + 59 * 4)

                                  = 30 * (2 + 236)

                                  = 30 * 238

                                  = 7140

Again, 3 + 7 + 11 + 15 + ........upto 60 terms

It forms an AP

Now, Sum of 2nd series = (n/2) *{2a + (n - 1)d}

                                  = (60/2) * {2 * 3 + (60 - 1)4}

                                  = 30 * (6 + 59 * 4)

                                  = 30 * (6 + 236)

                                  = 30 * 242

                                  = 7260

Now, sum of series upto 120 terms = 7140 - 7260

                                                           = -120