Suppose that the number of terms in an A.P. i | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$ a _1, a _2, a _3, \ldots \ldots, a _{2 k }$
$\sum_{ r =1}^{ k } a _{2 r -1}=40, \sum_{ r =1}^{ k } a _{2 r }=55, a _{2 k }- a _1=27$
$\frac{ k }{2

Vedclass · Accepted Answer

$5$

Vedclass · Answer

$ a _1, a _2, a _3, \ldots \ldots, a _{2 k }$
$\sum_{ r =1}^{ k } a _{2 r -1}=40, \sum_{ r =1}^{ k } a _{2 r }=55, a _{2 k }- a _1=27$
$\frac{ k }{2}\left[2 a _1+( k -1) 2 dight]=40, \frac{ k }{2}\left[2 a _2+( k -1) 2 dight]=55,$
$d=\frac{27}{2 k -1}$
$a _1=\frac{40}{ k }-( k -1) d =\frac{55}{ k }- kd$
$d =\frac{15}{ k } \Rightarrow \frac{27}{2 k -1}=\frac{15}{ k } \Rightarrow 9 k =10 k -5$
$	herefore k =5$

Suppose that the number of terms in an $A.P.$ is $2 k$, $k \in N$. If the sum of all odd terms of the $A.P.$ is $40 ,$ the sum of all even terms is $55$ and the last term of the $A.P.$ exceeds the first term by $27$ , then $k$ is equal to

Similar Questions

If $\frac{{3 + 5 + 7 + ..........{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + .........{\rm{to}}\;10\;{\rm{terms}}}} = 7$, then the value of $n$ is

If the sum of the series $54 + 51 + 48 + .............$ is $513$, then the number of terms are

If ${\log _5}2,\,{\log _5}({2^x} - 3)$ and ${\log _5}(\frac{{17}}{2} + {2^{x - 1}})$ are in $A.P.$ then the value of $x$ is :-

Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$

Let $S_n$ be the sum to n-terms of an arithmetic progression $3,7,11, \ldots \ldots$. . If $40<\left(\frac{6}{\mathrm{n}(\mathrm{n}+1)} \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{S}_{\mathrm{k}}\right)<42$, then $\mathrm{n}$ equals