1) 2, 2 1/2, 3 1/3,... I thought the nth term here was (2^n+n-1)/n. That gave me 19/4 as the fourth term but the answer is 5.
2) 2, 2 1/2, 3 1/8,... No idea. The answer is given as 3 2/3 9/2 (it's a typo, I guess). Maybe it is 3 29/32.
Interesting thing is that these questions come under the section harmonic progression. I couldn't figure out why though. Help?
$\endgroup$1 Answer
$\begingroup$Answer for the first sequence : The numbers are the reciprocals of the numbers $$0.5\ 0.4\ 0.3\ 0.2$$ corresponding to the fractions $$\frac{5}{10}\ \frac{4}{10}\ \frac{3}{10}\ \frac{2}{10}$$ So, the original sequence is $$\frac{10}{5}\ \frac{10}{4}\ \frac{10}{3}\ \frac{10}{2}$$ This is the reason why it is called harmonic progression.
The second sequence is a geometric progression with quotient $\frac{5}{4}$, which gives $$2\ \frac{5}{2} \frac{25}{8}\ \frac{125}{32}$$, that is $$2\ 2\frac{1}{2}\ 3\frac{1}{8}\ 3\frac{29}{32}$$
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