Poles in a Pile Telephone poles are being stored in a pile with poles in the first layer, in the second, and so on. If there are layers, how may telephone poles does the pile contain?
Number of telephone poles in the pile
Number of poles in first layer is
Total number of layers
Number of poles decreases by as we move down the pile of poles.
Show that the number of poles in consecutive layers forms an arithmetic sequence and find sum of this arithmetic sequence to find number of poles.
Number of poles decreases by
Number of poles in first layer,
Number of layers,
So the number of poles in consecutive layers as move down the pile forms the sequence:
which is an arithmetic sequence with first term and common difference .
Hence the term is which gives the number of poles in layer
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