Question

Twelve iron poles are to be used for pillars, and the length forms an AP. If the third pole is 4m and the seventh is 10m, find the length of the poles in order of the AP and the cost of the poles if a meter costs 450.

Answer 1

To find the lengths of the poles in an arithmetic progression, use the provided lengths of two of the poles to determine the common difference, then find the first term. List all pole lengths and sum them to calculate the total cost.

Step-by-step explanation:

The student is required to determine the lengths of twelve iron poles forming an arithmetic progression (AP) and calculate their total cost given the cost per meter. We know the length of the third pole is 4 m and the seventh pole is 10 m. To find the common difference d, we calculate:
10 = 4 + (7 - 3)d
6d = 6
d = 1

Now that we have the common difference, we can find the length of the first pole, which is the third pole minus twice the common difference (as it is two positions before the third pole in the sequence of the AP):
First pole length = 4 - 2(1) = 2 m

With the common difference and the first term, we list the lengths of the poles and calculate the total cost:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
To get the total length sum the series: 2 + 3 + ... + 13 = 90 meters.

Therefore, the total cost for the poles is:
Cost = Total length × Cost per meter
Cost = 90 m × 450 per m
Cost = 40500