Asked by mychelle
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?
Answers
Answered by
Damon
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
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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