Each term of a sequence, after the first term, is inversely proportional to the term preceding it, and the constant of proportionality stays the same. if the first term is 2 and the second term is 5, what is the 12th term?

The 12th term of the sequence is 5.

Step-by-step explanation:

Inversely proportional relation:

It can be written as

where, k is constant of proportionality.

First term is 2 and second term is 5. It is given that after first term, each term is inversely proportional to the term preceding it, and the constant of proportionality is same. It means

Multiply both sides by 2.

The constant of proportionality for given sequence is 10.

Subsequent terms will alternate between  2 and 5, with the odd terms being 2 and the even terms being 5.

12th term is an even term, so

Therefore the 12th term of the sequence is 5.

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