The value of $\sum\limits_{r = 1}^n {\log \left( {\frac{{{a^r}}}{{{b^{r - 1}}}}} \right)} $ is
$\frac{n}{2}\log \left( {\frac{{{a^n}}}{{{b^n}}}} \right)$
$\frac{n}{2}\log \left( {\frac{{{a^{n + 1}}}}{{{b^n}}}} \right)$
$\frac{n}{2}\log \left( {\frac{{{a^{n + 1}}}}{{{b^{n - 1}}}}} \right)$
$\frac{n}{2}\log \left( {\frac{{{a^{n + 1}}}}{{{b^{n + 1}}}}} \right)$
The sum of $n$ arithmetic means between $a$ and $b$, is
Shamshad Ali buys a scooter for $Rs$ $22000 .$ He pays $Rs$ $4000$ cash and agrees to pay the balance in annual instalment of $Rs$ $1000$ plus $10 \%$ interest on the unpaid amount. How much will the scooter cost him?
If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this $A.P.$ is :
The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$, the number of terms is
If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of last and first term is $273$, then the numbers are