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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Homework Help: Help on arithmetic sequence problem

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