use the formula for the general term of an arithmetic sequence
the terms would be
a, a+d, a+2d, a+3d, and a+4d
adding them up: 5a + 10d = 100
or a + 2d = 20 after dividing by 5
given:
sum of 3 largest equals seven times the sum of the two smallest, or
a+2d + a+3d + a+4d = 7(a + a+d)
3a + 9d = 14a + 7d
2d = 11a
from first equation a = 20 - 2d
into the second:
2d = 11(20-2d)
2d = 220 - 22d
24d = 220
d = 220/24 = 55/6
subbing back: a = 20 - 2(55/6) = 5/3
checking:
first term is 5/3 or 10/6
is 10/6 + 65/6 + 120/6 + 175/6 + 230/6 equal to 100 ?
YES!
divide 100 loaves of bread amoung 5 men so that the amounts are in arithmetic progression ( increase by the same amount each time) and the sum of the three largest shares is seven times the sum of the two smallest.
4 answers
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