# Twelve iron poles are to be used for pillars and the lengths of the pole form an A.P if the 3rd Pole is 4m and the 7th pole is 10m.Find the

A): Length of the pole in order of the A.P.
B): Cost of all the poles if a metre cost #45.

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1. 3rd Pole is 4m ----> a + 2d = 4
the 7th pole is 10m --> a + 6d = 10
subtract those two equations:
4d = 6
d = 6/4 = 3/2

back in a + 2d = 4
a + 2(3/2) = 4
a + 3 = 4
a = 1

Pole(n) = 3 + (n-1)(3/2)
= 1 + (3/2)n - 3/2
= -1/2 + 3/2 n
= 1/2 (3n - 1)

for the cost, you need the sum of the length of 12 poles
that is,
1 + 5/2 + 4 + 11/2 + 7 + .... + 35/2
= 6(first + last_
= 6(1 + 35/2) = 111 metres is your total length
each metre costs 45, so
just do 45*111

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