The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be

If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then

A man starts repaying a loan as first instalment of $Rs.$ $100 .$ If he increases the instalment by $Rs \,5$ every month, what amount he will pay in the $30^{\text {th }}$ instalment?

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and product of remaining two middle term is $15$, then greatest number of the series will be

The Fibonacci sequence is defined by

$1 = {a_1} = {a_2}{\rm{ }}$ and ${a_n} = {a_{n - 1}} + {a_{n - 2}},n\, > \,2$

Find $\frac{a_{n+1}}{a_{n}},$ for $n=1,2,3,4,5$

What is the $20^{\text {th }}$ term of the sequence defined by

$a_{n}=(n-1)(2-n)(3+n) ?$