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
$5$
$7$
$9$
$11$
The number of terms in an $A .P.$ is even ; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$ , then the number of terms in the $A.P.$ is
The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is
If the ${n^{th}}$ term of an $A.P.$ be $(2n - 1)$, then the sum of its first $n$ terms will be
A farmer buys a used tractor for $Rs$ $12000 .$ He pays $Rs$ $6000$ cash and agrees to pay the balance in annual instalments of $Rs$ $500$ plus $12 \%$ interest on the unpaid amount. How much will the tractor cost him?
If the variance of the terms in an increasing $A.P.$, $b _{1}, b _{2}, b _{3}, \ldots b _{11}$ is $90,$ then the common difference of this $A.P.$ is