The $8^{\text {th }}$ common term of the series $S _1=3+7+11+15+19+\ldots . .$ ; $S _2=1+6+11+16+21+\ldots .$ is $.......$.
$150$
$151$
$152$
$153$
Insert five numbers between $8$ and $26$ such that resulting sequence is an $A.P.$
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 $11,$ then find the number of terms.
The ${n^{th}}$ term of an $A.P.$ is $3n - 1$.Choose from the following the sum of its first five terms
If $\log 2,\;\log ({2^n} - 1)$ and $\log ({2^n} + 3)$ are in $A.P.$, then $n =$
If ${S_1},\;{S_2},\;{S_3},...........{S_m}$ are the sums of $n$ terms of $m$ $A.P.'s$ whose first terms are $1,\;2,\;3,\;...............,m$ and common differences are $1,\;3,\;5,\;...........2m - 1$ respectively, then ${S_1} + {S_2} + {S_3} + .......{S_m} = $