Question 1109475: Twelve iron poles are to be used for pillars and the lengths of the poles from an Arithmetic progression. If the third pole is 4m and the seventh is 10m, find the; (a) lengths of the poles in order of A.P.
(b) cost of all the poles if a metre costs 45.00naira.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! (a) the formula for the nth term of an arithmetic progression is
:
x(n) = a + d(n-1), where a is the first term and d is the common difference
:
we are given
:
4 = a + d(3-1)
10 = a + d(7-1)
:
simplify both equations
:
(1) a + 2d = 4
(2) a + 6d = 10
:
we two equations in 2 unknowns
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solve equation 1 for a
:
a = 4 - 2d
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substitute for a in equation 2
:
(4 - 2d) + 6d = 10
:
4d = 6
:
d = 6/4 = 1.5
:
using equation 1
:
a + 2(1.5) = 4
:
a + 3 = 4
:
a = 1
:
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the arithmetic progression for the pole heights is
:
1m, 2.5m, 4m, 5.5m, 7m, 8.5m, 10m, 11.5m, 13m, 14.5m, 16m, 17.5m
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(b) the formula for the sum of the first n terms of an arithmetic progression is
:
s(n) = (1/2) * n * (first term + the last term)
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we want to sum the first 12 terms
:
s(12) = (1/2) * 12 * (1 + 17.5) = 111m
:
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cost of all the poles is 111m * 45.00naira per m = 4995.00naira
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