# algebra 2

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An arithmetic progression has 5 terms that have a sum of 200. The sum of the last three terms added to 6 times the sum of the first two terms equals zero. What is the first term?

• algebra 2 -

a1 + a2 + a3 + a4 + a5 = 200

6 (a1 + a2) + a3 + a4 + a5 = 0

a1 = a1
a2 = a1 + m
a3 = a1 + 2m
a4 = a1 + 3m
a5 = a1 + 4m
so

5 a1 + 10m = 200
6(2 a1+ m) + 3 a1 + 9m = 0

a1 + 2 m = 40
15 a1 + 15 m = 0

m = -a1

a1 - 2a1 = 40
a1 = -40
m = 40

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