If the sum of three numbers of a arithmetic sequence is $15$ and the sum of their squares is $83$, then the numbers are
$4, 5, 6$
$3, 5, 7$
$1, 5, 9$
$2, 5, 8$
Suppose that all the terms of an arithmetic progression ($A.P.$) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6: 11$ and the seventh term lies in between $130$ and $140$ , then the common difference of this $A.P.$ is
${7^{th}}$ term of an $A.P.$ is $40$, then the sum of first $13$ terms is
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=2^{n}$
If $1,\,\,{\log _9}({3^{1 - x}} + 2),\,\,{\log _3}({4.3^x} - 1)$ are in $A.P.$ then $x$ equals
Find the sum of odd integers from $1$ to $2001 .$