What is the Sum of the First 110 Terms in This Arithmetic Progression?

[demonelite123]

If the sum of the first 10 terms and the sum of the first 100 terms of a given arithmetic progression are 100 and 10, respectively, what is the sum of first 110 terms?

S(10) = (10/2) (a1 + a10) = 100
S(100) = (100/2) (a1 + a100) = 10

a1 + a10 = 20
a1 + a100 = 0.20

a100 = a1 + 99d
a10 = a1 + 9d

i subtracted and got:
a10 - a100 = 19.8
a1 + 9d - a1 - 99d = 19.8
d = -0.22

S(110) = (110/2) (a1 + a110)
a110 = a100 + 10d

S(110) = 55 (a1 + a100 - 2.2) = 55(0.20 - 2.2) = 55(-2) = -110

is this correct?

 

[Unco]

If the sum of the first 10 terms and the sum of the first 100 terms of a given arithmetic progression are 100 and 10, respectively, what is the sum of first 110 terms?

S(10) = (10/2) (a1 + a10) = 100
S(100) = (100/2) (a1 + a100) = 10

a1 + a10 = 20
a1 + a100 = 0.20

a100 = a1 + 99d
a10 = a1 + 9d

i subtracted and got:
a10 - a100 = 19.8
a1 + 9d - a1 - 99d = 19.8
d = -0.22

S(110) = (110/2) (a1 + a110)
a110 = a100 + 10d

S(110) = 55 (a1 + a100 - 2.2) = 55(0.20 - 2.2) = 55(-2) = -110

is this correct?

Yes; well done!