Explain why the precise length target DNA sequence doesn't get amplified until the third cycle?

Answer 1

In the first polymerization step, a new DNA strand is synthesized onto each primer.
Taq polymerase extends this new strand well beyond the target sequence,
producing a new DNA strand that contains the downstream/upstream primer and
is longer than the target.
In the second cycle, the DNA is denatured and primers anneal to the original target
DNA and to the new DNA strands produced in the first cycle. A mixture of small
target sequences and larger hybrid DNA sequences are produced at the end of the
second cycle.
In the third cycle, the target DNA of defined length is reprimed with both upstream
and downstream primers. Taq polymerase then synthesizes two copies of target
DNA of defined length. The number of these defined target sequences is doubled
with each subsequent round of PCR, thereby increasing logarithmically. Thus, a 40
cycle PCR would amplify a given template 240
, thus potentially producing 1.0 x 1012
DNA molecules.
In the first polymerization step, a new DNA strand is synthesized onto each primer.
Taq polymerase extends this new strand well beyond the target sequence,
producing a new DNA strand that contains the downstream/upstream primer and
is longer than the target.
In the second cycle, the DNA is denatured and primers anneal to the original target
DNA and to the new DNA strands produced in the first cycle. A mixture of small
target sequences and larger hybrid DNA sequences are produced at the end of the
second cycle.
In the third cycle, the target DNA of defined length is reprimed with both upstream
and downstream primers. Taq polymerase then synthesizes two copies of target
DNA of defined length. The number of these defined target sequences is doubled
with each subsequent round of PCR, thereby increasing logarithmically. Thus, a 40
cycle PCR would amplify a given template 240
, thus potentially producing 1.0 x 1012
DNA molecules.

Answer 2

This occurs because in each of the first two cycles, only two strands are made. By the third cycle, six partial DNA strands are produced, with two of them having the original DNA and a long synthesized strand, as well as a pair with a long synthesized strand and strand with the target sequence, and two double stranded products of the target sequence.

Answer 3

During the first two cycles of PCR, the primers bind to the target DNA sequence, but not enough copies are made to be detectable. It is only by the third cycle that the amplification reaches a level where the target DNA sequence becomes noticeable.