If the ${p^{th}}$ term of an $A.P.$ be $\frac{1}{q}$ and ${q^{th}}$ term be $\frac{1}{p}$, then the sum of its $p{q^{th}}$ terms will be
$\frac{{pq - 1}}{2}$
$\frac{{1 - pq}}{2}$
$\frac{{pq + 1}}{2}$
$ - \frac{{pq + 1}}{2}$
Let $S_n$ denote the sum of first $n$ terms an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15}-$ $S_5$ is:
The sum of $n$ terms of two arithmetic progressions are in the ratio $(3 n+8):(7 n+15) .$ Find the ratio of their $12^{\text {th }}$ terms.
The sum of the first and third term of an arithmetic progression is $12$ and the product of first and second term is $24$, then first term is
Let the digits $a, b, c$ be in $A.P.$ Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in $A.P.$ at least once. How many such numbers can be formed?
A manufacturer reckons that the value of a machine, which costs him $Rs.$ $15625$ will depreciate each year by $20 \% .$ Find the estimated value at the end of $5$ years.