The number of terms common between the two series $2 + 5 + 8 +.....$ upto $50$ terms and the series $3 + 5 + 7 + 9.....$ upto $60$ terms, is
The number of terms common between the two series $2 + 5 + 8 +.....$ upto $50$ terms and the series $3 + 5 + 7 + 9.....$ upto $60$ terms, is
- A
$18$
- B
$20$
- C
$22$
- D
$24$
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If $^n{C_4},{\,^n}{C_5},$ and ${\,^n}{C_6},$ are in $A.P.,$ then $n$ can be
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Let $S_{1}$ be the sum of first $2 n$ terms of an arithmetic progression. Let, $S_{2}$ be the sum of first $4n$ terms of the same arithmetic progression. If $\left( S _{2}- S _{1}\right)$ is $1000,$ then the sum of the first $6 n$ terms of the arithmetic progression is equal to:
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- [JEE MAIN 2021]
For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,
Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd.
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Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd.
Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer
Write the first five terms of the following sequence and obtain the corresponding series :
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Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}, n\, \geq\, 2$